I'm so sorry, it sounds like a nightmare. DD has periodic girl troubles (with one girl in particular), but I actually think some of it is dd's fault because she gets upset too easily. I just keep telling her that if she did anything wrong, apologize, and hope the other girl is mature enough to do the same. If not, is the girl really friend material? Focus on the girls who respect you and actually want to be your friend. You said your DD can name some nice girls. Tell her to focus her efforts on those girls. Eventually maybe she could get their phone number and talk on the phone.
When DD had the last episode with a certain girl, I waited about a week to see if the two of them could figure it out, and then when it appeared they wouldn't be able to, I emailed the teacher and suggested the teacher tell the girls "I noticed you two are having problems getting along lately. I think we should sit down and the two of you have a discussion about how things can be better." The teacher replied and said she had been planning on doing that but didn't get a chance. She sat the girls down and asked the other girl "What could be done to make things better?" and the other girl said "Nothing." Teacher sat them down again the next day and asked what they both expect in a friend, and then I guess they reconciled. Now they are friends again. DD was orignially horrified by the notion of getting the teacher involved, but I think there are ways to do it so that it doesn't look like your DD is a tattle-tale.
If it seems like nothing is going to improve, then figure out if it will be the same everywhere and your DD just needs some social skills training, or if it just that school and your dd's place in the hierarchy. I wouldn't keep her long-term in a situation where she's unhappy and there is little hope of improvement.
