M.J.
I wish I was writing with a wonderful fix all solution, however I have 3 daughters all 4-5 years apart with the oldest being 11 and your house sounds like a replica of mine. My oldest acts like her younger sister is not as good as the dirt she walks on and she treats her youngest sister only slightly better, and we quit letting her have company over because of the way she treats them both when she does. I think it's the age and quiet possible the age difference. At these ages their likes and dislikes are vastly different and the oldest ones are starting to want their own privacy, more privaledges like a later bedtime, etc.
The only consolation is that I am from a family of five girls and we all get along famously now.
Good luck and try not to pull all of your hair out!
M.