Twice in your post you mention activities outside school:
"I try to encourage her to play sports or take art lessons, etc. She needs a hobby I think.
I'm hoping I can get my girls involved in activities of some kind and move on to better days."
So it sounds like your girls are not really involved in anything but school and their friends, which is a recipe for drama at this age. You're right: Keep them busy and they have less time for drama. Your older girl can't be on the phone making comments that end with parents calling YOU if she is very busy. By age 11 she should have plenty of homework to do; if she doesn't, get with the teachers to ask why. And yes, help her find some activities outside school that really interest her -- it does not have to be a sport because by age 11 many kids have played competitive sports for years and those avenues are kind of closed to newcomers, but get HER involved iin choosiing something. If she likes art, find art classes; dance, find dance classes; or more unusual sports like archery or fencing or whatever! Cultivate friends for her in those places.
It is typical at 11 to have friend drama. Don't push her too hard to get along with everyone, all the time, or to maintain friendships that are drifting away from her, even if the friend has ben a "lifelong BFF" -- that doesn't matter much at this age, sometimes. Be active in knowing other girls in her class (and her new activities) and ask her which of those girls she wants to have come over to your house. Or take her and some newer girl she knows out for ice cream, or whatever.
But do keep her busy and let her find things she likes to do. She will develop friendships based on a shared interest in a common activity, and that is much better than friendships based on "we've known each other around the neighborhood" or "we hang out at recess."