M.B.
I have a similar situation, my husbands oldest sister & I don't get a long, and haven't in the 14yrs we've been together. I felt for years she was trying to compete against me, (she almost 43 & dress' and acts like she is 20, & not married). I finally laid it out a few years ago. I told her you are his sister & always will be, I am his wife, that shouldn't be any reason to try to compete for his attention, if for some reason we get divorced, you will still be in his life. If you don't like me fine, at least treat me with the same respect you want me to give you.
Since you both have children, maybe let her know that it is important for the children to get along, and let her know that when you all have to get together, she doesn't have to go out of her way to be extra nice, at least not be negative, kids pick up on this, & would hate for them to grow up hating their cousins/family & for no reason at all. Small talk helps too, that way you can always say you tried.
Good luck & hope things work out.
M.