I have a similar relationship with my SIL.
I think the best way to summarize your situation is that it sounds like you are just two different people, with two different parenting styles and you will likely never be friends. Once you can accept those facts, perhaps you can just get along with her and her family?
Face it, you probably wouldn't be "friends" with her and her daughter unless you married your husband. Maybe she feels like "they" came first and don't have to change for anyone. Perhaps it's hard for her to "share the spotlight" with your daughter - maybe her daughter got all of "Uncle ____" attention before you and your daughter came along?
I have found that the best way to "get along" with my sister in law is to give a lot of "un huh" (yes) to whatever she says, to mostly ignore my nephew's behavior and to not offer up ANY personal advice, suggestions or information.
I realize this isn't an ideal situation and I dearly wish my answer was different. However I think some people just don't gel. And trying to force the issue is just going to make everyone miserable.
Let the girls play together when the family is together. Send her a card in the mail for her birthday and other holidays. Be the bigger person.
Don't spend time with her, them (as a couple) or the family unless it's a family gathering with other relatives. It's just going to be "difficult".
Some families gel great. Some do get along. Others, not so much.
Just know that if YOU try to be civil, be her friend, invite them out on couples dates, etc. then YOU don't get to complain to your husband about how rude they are, how much they complain, how they treated you or your child, etc. If YOU are going to take that on, then YOU have to learn how to deal with their behavior.
Personally, I have opted out. I have chosen to be nice/civil with no extras. I have accepted that my SIL and I will never be "friends", so I've stopped trying. And actually, we get along better now that we only need to be "nice" to each other at holiday/family parties.
I hope you find some peace.