Your husband's brother is such a nice guy yet you just cannot seem to get his wife to like you. It would be great if everyone could get along yet she refuses to give you a fair chance. She is very nice towards your husband and the rest of his family. You try to bond with her but she refuses all of your attempts. She is too busy disliking you for "stealing her spotlight". She is no longer the only daughter-in-law in the family, she has to share the spotlight with you which is something that she does not want to do. She feels competition, jealousy and anger towards you and will do anything to make you feel stupid and unwelcome.
Just know that you have done nothing wrong. Do not go out of your way to kiss her behind. She was once in your shoes. She had to go through meeting the same family and has had similar experiences as the newcomer once she married your brother in law. It is unlikely that anyone treated her in the same way that she is treating you so do not blame yourself. She has no right to make you feel uncomfortable.
Steps:
Stand up for yourself: You are a part of the family now. Your husband chose you to be his wife. You have every right to be included as a part of this new family. Building a relationship with your in-laws is very important so do make the effort to visit often, get closer.
Socialise with your brother-in-law and his wife. You and your husband should invite his brother and his wife for dinner or go out on a double date. Use the outing as an opportunity to break the ice.
If your new brother-in-law and his wife reject your offer to meet for dinner then just stop trying. Give them some time and space. Realise that there is nothing left to give. You can only try so long before your patience runs out.
Make a decision on how to deal with it. Your brother-in-law's wife goes out of her way to make you feel uncomfortable. She rolls her eyes at you and she gossips behind your back. The best thing to do is ignore this.
Discuss everything with your husband. Let him know that you are aware that his sister-in-law does not like you. Also explain to him how much it hurts you that she goes out of her way to make you feel uncomfortable. He does not have to 'fix' the problem for you.
Do not allow this jealous witch to interfere with the opportunity of you getting to know your in-laws. You have every right to build a relationship with your mother-in-law and father-in-law. Do not be intimidated.
If your brother-in-law's wife continues to be uncivilized then do not be afraid to approach her with a stern attitude. Let her know that you are aware of how she feels and that you do not appreciate her approach on the situation. Let it be known to everyone in your husband's family.
Stand your ground. If anyone in your husband's family is purposely excluding you from family events, especially for the sake of his sister-in-law, then show up with your husband anyway. Let them know that you are a couple and that you will not stay back.