I think it might be time to reconsider the public schools and go and talk to the principals about your situation. You might be surprised and a talk is only that - not a commitment to enroll her. A school that actively excludes her sounds awful.
Does the more expensive private school offer athletics scholarships?
i totally agree with this.

i also think that trying to initiate a conversation with anyone at her current school may not have a lot of success as there is a fair chance they will be defensive & not admit anything was wrong. i think the way they're behaving is completely out of order & even if a student is considered more difficult then you think they'd be happy to have something at which the student is doing well & seems to enjoy & want to develop her interest. if that is the way they treat students, i don't think it's a great place for your daughter to learn & grow. perhaps there is some sort of scholarship to the other private school (never hurts to ask or chat to them) or you may find the public school is a better environment than expected.