There's something else I thuoght of, OP, that might be helpful. When mine were small and the oldest started to pick at her little sister (they are 5 years apart), I said, "You know, you are the kind of girl you are because of the way Daddy and I treated you. You will grow up to be a particular kind of person because of what we taught you. But your sister is going to have not only Daddy and me, but you, to watch and learn from. If you want her to always be annoying to you, then you keep picking at her and making fun of things she can't do as well as you, or arguing because she wants something that is yours. But if you want a sister you can call on the phone and have fun with when you are old ladies after Daddy and I are gone, you need to understand that you are starting that relationship right now when you are children. So you decide which kind of sister you want when you get older - one who avoids you and won't ever be there for you or one that is close and a blessing in your grownup life?"
Boy, for some reason it was putting it in those terms that worked. I am so happy about the relationship my DDs have - they often have "sister time" wnen DD19 gets home on a college break - they go to dinner and a movie, or shop, or watch videos in bed together. But I did have to nip some of that girl fighting stuff in the bud when they were younger.