It sounds like a situation that has been percolating for awhile (based on your post). There is some drama, and the girls get upset with one another. The school may be trying to reduce drama by separating the girls-- which works great in Kindergarten, but not 4th grade. They don't have a great reason (outright bullying) to separate the girls, but it sounds like they are sucking up a lot of energy.
I've noticed that you posted in twice-exceptional. I didn't see where you mentioned a dual diagnosis for your DD. I'm sorry if I missed it. My DS has ADHD and a diagnosis for social pragmatics. Often, he does not "read the room" in terms of social cognition. He gets the details, but misses the big picture, which means no matter who is doing what first, he always gets caught. It causes him to feel picked on-- but in fact, his classmates are showing some savvy social skills that he lacks. It was really hard for me to come to terms with regarding fairness, but once I sat down with his therapist I understood that my son's peers have a social survival skill that he does not (gestalt processing).
Keep in mind that teachers, administrators, etc. aren't always great about understanding the full context either. They are trying to keep the peace in environments where (IMO) bullying is not well understood as a pattern of malicious behavior, not an accidental playground shove or an occasional mean word. Unfortunately, a lot of parents don't understand it either, and will intervene over some pretty minor stuff. I'm not saying that bullying isn't a problem, but when my son mentions unkindness (he's on the receiving end quite a bit), I ask about context, patterns of behavior, and how (or if) it was resolved by teachers. We've uncovered some mean words/attitudes (which need to be addressed as part of school culture), but only a few situations of ongoing behavior or an egregious act by another student.
I don't know if any of this helps- I get that relationships with teachers and administrators can feel yucky. They don't necessarily "get" your kid and in the process of keeping peace for all, they can be punitive toward one. We have this happen- my son is the one asked to move desks, stay in from recess, sit out, etc., for what is really a "dynamic" with teachers and other kids, not just a problem that he alone created. It sucks (can we say that here?), it really does. It's hard to defend him because I either have to lay it all on his special needs or go on the offense with teachers and other students (not a great move for collaborative relationships). My advice, stay neutral-- advocate for your daughter's needs, but require a clear run down of behaviors. Who, what, where, when, and why. I've found that my DS isn't the problem as often as represented, but he is frustrating to others so can tend to be the focus. I call teachers out on that.
Good luck.
