In His Name The Most High
Peace and Benedictions Upon Muhammad and his Household.
__________________________________________
The Fundamentals of Religion (Usulu Deen) in Shi'a interpretation of Islam is Three:
1. Tawhid (Oneness of God)
2. Nubuwah (prophethood)
3. Maad (Resurrection).

However, the inseparable part of Tawhid is "al-Adl Illahi" - Justice of God; while that of Nubuwah is "al-Imamah" (Divine Leadership/guardianship). These two inseparable parts also form the bed-rock of Shi'a belief. In sha Allah as the topic suggests, I shall limit myself to the concept of Imamah.

VERSE OF AL-IMAMAH
"And when Ibrahim was tried by his Lord with some statements, and he fulfilled them, He said, 'I will appoint you an IMAM of mankind.' He (Ibrahim) asked, 'And of my offspring?'. He (Allah) replied, 'My Covenant shall not reach the wrongdoers"
~Quran 2:124

Ibn Kathir comments:
"...When he fulfilled the huge obligations which his Lord commanded him with, he appointed him the Imam of mankind, whom they must follow, and whose guidance they must copy. He requested Allah that this Imamah be connected with his lineage, and be uninterrupted within his offspring, and be perpetual forever among his offspring. So, what he asked WAS GRANTED, and he was granted full authority of Imamah, and the wrong-doers were excluded from its reach and it was made exclusive to the righteous scholars among his offspring."
~Abu al-Fida Ismail ibn Kathir, 'Qisas al-Anbiya', vol. 1 p. 232; 'al-Bidayah wa al-Nihayah', vol. 1 p. 191.

"Offspring/Family of Ibrahim?"
"Verily, Allah chose Adam, Nuh, the Family of Ibrahim and the family of Imran above the worlds..." ~al-Imran:33

Imam Bukhari (d. 256H) writes:
"{Verily, Allah chose Adam, Nuh, the family of Ibrahim and the family of Imran above the worlds...Allah provides sustenance to whom He wills, without limit}. Ibn Abbas said: "{and the family of Imran} They are the believers from the family of Ibrahim, the family of 'Imran, the family of Yasin AND THE FAMILY OF MUHAMMAD..." ~Sahih al-Bukhari, Vol. 3 p. 1263

Imams Are From The Ahl al-Bayt
Sunni Imam, Abu Ya'la (d. 307H) records:
...Anas reported: "The Messenger of Allah, peace be upon him, said: 'The Imams are from Quraysh"
~Abu Ya'la Ahmad b. Ali b. Muthana al-Mawsili al-Tamimi, 'Musnad vol. 6 p. 321

The annotator (of the Musnad), Dr. Husayn Salim Asad says: "Its chain is sahih."

Al-Hafiz Ibn Hajar al-Asqalani (d. 852H) declares:
"The hadith 'The Imams are from Quraysh' is recorded by al-Nasai from Anas, and al-Tabarani narrated it in al-Du'a, and al-Bazzar and al-Bayhaqi also narrated it, through several chains, from Anas. I say: I gathered its chains in a separate volume from forty sahabah" ~Ibn Hajar, 'Talkhis al-Habir, vol. 4 p. 116 #1730.

Note: This hadith is similar in context and meaning with another hadith vastly recorded by Imam Bukhari and Imam Muslim and Imam Ahmad et al in their Sahih and Musnad respectively:

"The Khalifa (in other version, the word 'Amir' is used) after me will be TWELVE; all of them from Quraysh"

Quraysh is however a very Big clan with several families constitute the Clan. The two prominent families were Banu Hashim (the family of the holy prophet) and Banu Umayyah, an age-long rival. The office of Imamah is too sensitive in its functions ('Guide of Mankind' according to Quran) to be left at the hands of Qurayshite Clan to choose who assume the office at an appointed time owing to the fact that there were too many wrongdoers among them as a whole. Allah clearly declares when He laid the foundation of Imamah:
"...'My Covenant shall not reach the wrongdoers"
~Quran 2:124

Al-Tabari records with Sahih chain from Mujahid that he said: (My Covenant shall not reach the wrongdoers) There will never be an Imam who does wrong.

The Merits and Praise of the 'household (ahl al-bayt) of the holy prophet (peace be upon him and his household) are too numerous and outstanding to be compare with ANYBODY in the prophet's community; hence, the prophet (peace be on him and his household) himself declares in his last will:

The holy prophet (peace be on him and his family) gathered his Ummah in his last Hajj at Arafat, Ghadir Khum and on his death-bed, he proclaimed:

"I am leaving behind over you TWO WEIGHTY THINGS so long you adhere to them, you will NEVER go astray; the Book of Allah - a rope stretching between the heaven and the earth - and my offspring, my Ahl al-Bayt. Verily, both shall never separate from each other until they meet me at the Lake-Fount"
~Muslim, Tirmidhi, Ibn Majah, Abu Dawud, Ahmad Ibn Hanbali, Abu Ya'la, Tabarani, Hakim, Suyuti et al.

Allamah Nasir Deen al-Albani in his "Sahih al-Jami' al-Saghir wa Ziyadatuhu (Al-Maktab al-Islami), vol. 1 p. 482, hadith no. 2457 records the holy prophet (peace be on him and his family) to have said yet in another version of hadith thaqalain called 'hadith Khalifatain':

"I am leaving behind over you TWO KHALIFAHS; the Book of Allah - a rope stretching between the heaven and the earth - and my offspring, my Ahl al-Bayt. Verily, both shall never separate from each other until they meet me at the Lake-Fount"

Then, Sheik (al-Albani) comments: *Sahih.

These are FEW proves from the holy Quran and sahih Sunni traditions on the Concept of Imamah. Shi'a follow (in accordance with the hadith of 12 successors of the prophet as reported by Bukhari, Muslim, Ahmad et al) TWELVE Imams /Khalifa /Amir ONLY from the household of the holy prophet (peace be on him and his household).

The Prophet [peace be on him and his household]
said: 'Verily your Imams are your representatives before Allah, therefore be careful whom you follow in your religion and your prayers.'

~Al-Kafi vol.1, p.199, hadith no. 15
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Empiree:
Albaqir and tbaba1234 and others. Beautiful speech, isnt.
https://www.youtube.com/watch?v=2zx2lKAmv8U

Beautiful speech Indeed! I'm however surprise upon the sheik Imran's scholarstic understanding, boldly challenging the concept of Imamah and Khilafah of Ahli Muhammad (progeny of Muhammad) (peace be on him and his household) with its permanent restriction on this lineage in the light of 'clear verses' of the Qur'an and Sahih ahadith. Sheik even labeled the concept "Shi'a creation".

Sheik Adam Abdullah al-Ilory (ra) too challenged with the same thought of Sheik Imran Hussein.

It is obvious should they be convinced with the Imamah and Khilafah of the progeny of the Prophet (peace be on him and his household), then their entire belief, years of teachings, Jihad etc will collapse.

What they reject is what other prominent scholars (past and present) were (are) convinced of.
A sincere scholar studies carefully available presentations and argument and do not let even an atom of emotion preside or influence his judgment.
*************

Part of our Submission is @the OP, and we await a sincere researcher to counter it.

AlBaqir:
.

Khayr. I understand actually. May I have article or video clip of Sheik Adam(r) on this issue if you have one?. Honestly, I challenge it, too.

Do you get his methodology in this clip^? That's methodology i learned.

Empiree:
Khayr. I understand actually. May I have article or video clip of Sheik Adam(r) on this issue if you have one?.

I read it in one of baba Adam's tira long time ago.

Empiree:

Honestly, I challenge it, too.

Ma sha Allah! You are free and most welcome to present your opposing view as against the Op's submission.

Empiree:

Do you get his methodology in this clip^? That's methodology i learned.

Ma sha Allah. I do, and that has always been Sheik Imran's methodology. He always try to be in the mid-course. However, challenging the concept of Imamah as understood and explained by the Shi'a is invariably (calling it "shi'a creation" proven it to be Bid'ah. And Bid'ah leads to misguidance and misguidance leads to Hell. That's why both the Shi'a and opposites have to be extra careful and sincere in treating issues esp the fundamental beliefs that can make one a believer or a kafir.

A prominent Sunni Alim, the then Mufti of al-Ahzar University, Sheik Salim
al-Bishri dialogue with a Shi'a prominent scholar, Ayatullah 'Abd al-Hussein Sharafa deen al-Musawi in the 50/60s. Their conclusion was healthy to the point that the Mufti of al-Ahzar pass fatwa to include Imami fiqh (shi'a Jurisprudence) into effect.
http://en.m.wikipedia.org/wiki/A_Shi'i-Sunni_dialogue

# [size=15pt]HADITH KHALIFATAIN - NARRATIONS OF THE TWO CALIPHS[/size]

1. Imām al-Fasawī (d. 277 H) records:

‘Ubayd Allāh – Sharīk – al-Rukayn – Qāsim b. Ḥassān – Zayd b. Thābit:
The Messenger of Allāh, peace be upon him, said: “I am leaving behind over you MY KHALĪFAH: the Book of Allāh the Almighty and my offspring, my Ahl al-Bayt. Verily, both shall never separate from each other until they meet me at the Lake-Fount.”

Ref: {Abū Yūsuf Ya’qūb b. Sufyān al-Fasawī, al-Ma’rifah wa al-Tārīkh (Beirut: Dār al-Kutub al-‘Ilmiyyah) [annotator: Khalīl al-Manṣūr], vol. 1, p. 294}

2. Imam Ibn Abi Shaybah (d. 235 H):

Abū Dāwud ‘Umar b. Sa’d – Sharīk – al-Rukayn – al-Qāsim b. Ḥassān – Zayd b. Thābit – the Prophet:

“I have left behind over you the TWO ALL-COMPREHENSIVE KHALIFAHS: the Book of Allāh and my offspring. Verily, both shall never separate from each other until they meet me at the Lake-Fount.”

The annotators declare: The hadith is Sahih. It has Shawahid (witnesses).

Ref: Abū Bakr ‘Abd Allāh b. Abī Shaybah, Musnad Ibn Abī Shaybah (Riyādh: Dār al-Waṭan; 1st edition, 1418 H) [annotators: ‘Ādil b. Yūsuf al-‘Azāzī and Aḥmad b. Farīd al-Mazīdī], vol. 1, p. 108

3. Imam Ahmad (d. 241 H):

Abd Allāh (b. Aḥmad) – my father (Aḥmad b. Ḥanbal) – al-Aswad b. ‘Āmir – Sharīk – al-Rukayn – al-Qāsim b. Ḥassān – Zayd b. Thābit:

The Messenger of Allāh, peace be upon him, said, “I am leaving behind over you TWO KHALIFAHS: the Book of Allāh – a rope stretching between the heaven and the earth or from the heaven to the earth – and my offspring, my Ahl al-Bayt. Verily, both shall never separate from each other until they meet me at the Lake-Fount."

Ref: Abū ‘Abd Allāh Aḥmad b. Ḥanbal al-Shaybānī, Musnad (Cairo: Muasassat Qurṭubah [annotator: Shu’ayb al-Arnāūṭ], vol. 5, p. 181, # 21618

4. Imam Ibn Abi Asim (d. 287 H):

Abū Bakr – ‘Amr b. Sa’d Abū Dāwud al-Ḥafarī – Sharīk – al-Rukayn – al-Qāsim b. Ḥassān – Zayd b. Thābit:

The Messenger of Allāh, peace be upon him, said, “I am leaving behind over you the TWO KHALIFAHS after me: the Book of Allāh and my offspring, my Ahl al-Bayt. Verily, both shall never separate from each other until they meet me at the Lake-Fount.”

‘Allāmah al-Albānī (d. 1420 H) declares:

It is a ṣaḥīḥ ḥadīth. But, its chain is ḍa’īf due to the poor memory of Sharīk, and he was Ibn ‘Abd Allāh the Judge. Also, al-Qāsim b. Ḥassān is majhūl al-ḥāl (i.e. his status is unknown). The ḥadīth is recorded by Aḥmad (5/181-182, 189, and 190) through two other chains from Sharīk with it. I have only declared it ṣaḥīḥ because it has witnesses (shawāhid) that strengthen it.

Ref: Abū Bakr b. Abī ‘Āṣim, Aḥmad b. ‘Amr b. al-Ḍaḥḥāk b. Mukhlid al-Shaybānī, Kitāb al-Sunnah (al-Maktab al-Islāmī; 1st edition, 1400 H) [annotator: Muḥammad Nāṣir al-Dīn al-Albānī], vol. 2, pp. 350-351, # 754

5. Allamah Nasir Deen al-Albani also documents:

"I am leaving behind over you TWO KHALIFAHS; the Book of Allah - a rope stretching between the heaven and the earth - and my offspring, my Ahl alBayt. Verily, both shall never separate from each other until they meet me at the Lake-Fount."

Sheik al-Albani simply comments: * Sahih

Ref: {Sahih al-Jami al-Saghir wa Ziyadatuhu (Al-Maktab al-islami), vol. 1 p. 482, hadith no. 2457}

bismiLLaah wa solatu wa salam Alaa rosooliLLaah

Your response is in three phases

Firstly, the hadiths are weak with this wording because they all evolve round Sharik who is weak in memory,

He is Sharik bn AbdiLLaah the judge.
Muhammad bn Yahya Al Qattaan reported from his father said; I saw some muddling in Sharik's reports.

AbdulJabbaar bn Muhammad said; I saI'd to Yahya bn Sa'eed; some people think Sharik only muddled reports in his last days (i.e old age). He (Yahya) replied; "he was always a muddler.
AbduLLah bn Mubaarak said; The hadiths of Sharik are nothing.

Aljurjaaniyy said; (Sharik is) poor in memory, muddled up reports.

Ibrahim bn Sa'eed alJawhariyy said; Sharik erred in four hundred reports.
(reference; meezanul i'tidaal volume 2 page 270)
Ibn Hajar summarize's it all in his taqreeb; sodooq(trustworthy) mukhti (errs). (taqreeb number; 2802)
So Sharik is religiously upright but has poor memory. (may Allah have mercy on him pardon me and him).
So why did Imam Albany authenticate it?
It's stated in your post; "because it has witnesses". But it's only the first part that has witness not the second part.
The Quran asks us to follow Allah and his messenger alyhissolaat wassalaam, and adds the scholars in some places, it adds the companions in other places.
So, the second part is weak.

Secondly;
Even if we accept that the hadith is authentic, it is not an evidence that khilafah, belongs to the ahl bayt only.
The text of the hadith points to that;
Now ponder; two khalifahs, The Quran and my progeny.

The meaning of khalifah here can't be caliphate because the Quran can't be a caliph or explain to me how Quran becomes king and wears crown or things like that.
So the meaning of khalifah hear is that we honour them and respect them. Because khalifah is a word that is used for whoever or whatever you leave behind after departing, not necessarily a ruler (see mu'jamul waseet pg 275 under root word kha lam and fa).

Thirdly,
You grab firmly a narration that is barely reliable and disregard several other clear-cut authentic narrations that mentioned the virtues of Abu Bakr and Umar .

Examples;

Follow those after me; Abu Bakr and Umar (tirmidhi; 3663) (Soheehah; 1233)
....but Allah and His messenger (alyhissolaat wassalaam) and the believers reject (anyone) except Abu Bakr. (Soheeh Muslim; Book of virtues of companions, chapter of virtues of Abu Bakr)

Lastly but definitely not the least;

The messenger of Allah alyhissolaat wassalaam said;
indeed the first of your religion is prophethood and mercy, then khalifah and mercy, then it will be kingship and oppression. (haythamiyy in alMujma' 5/189) Imam Suyooti said in tarikhul khulafa (published by darul ghaddil jadeed) pg 23 (hadith Hasan)

Definitely the first part mentioned here is the leadership of the Prophet Muhammad alyhissolaat wassalaam.
Then hadith is one of the signs of the Prophet's genuine prophethood. alyhissolaat wassalaam

The second part of isla-group it anyway you like- includes the khilafah of Abu Bakr and Umar.
so they are bona-fide khalifah and the Messenger alyhissolaat wassalaam described them as merciful.

Now tell me why the Messenger didn't order Ali to the Solah while on his death bed..

^ see reply:
https://www.nairaland.com/3051297/concept-imam-ship-caliphate-true#44810309