Tau

Were I in your shoes, I would keep talking with her. Discover what the difference is between the class at school and the class at the studio.

If it comes down to being in a safe place - find out if there are compromises. What if you have the teacher over for dinner, if you sit in the class in the back, etc... What would make her feel safe? (and ask her that)

If she continues to stress that nothing will help, then let her know that its up to her, but then she will lose the class. Give her the power to choose, and it might be enough to brave it out.

Otherwise I would keep her home until shes old enough to try things alone. I believe its potentially damaging to push kids into situations they aren't ready for. Continue to give them the opportunity, talk about the pros and cons, and they will set the course that is the most appropriate for them.

YMMV.