How do the sisters treat each other in Mansfield park? Does the status of each play a role in this?

By sisters, I'll answer for Maria and Julia, since that is a main focus. Usually they're the best of friends and leave Fanny out. They play games and go to school together. But when they grow up and Henry comes they become rivals for his affection. It's a constant back and forth, with Maria mostly coming on top. This is because she thinks that as an engaged woman she is safe. The opposite is true though. She would be talked about in a way that would damage her reputation. After Henry is gone, they are the best of friends once more. Julia even goes with her sister on her honeymoon.