I'm with Laurie. They should refund your deposit, and chances are that you can return the shoes she hasn't used yet. My daughter was in competitive cheer for a year, and that's a huge time commitment, and then competitive gymnastics AND competitive dance, too? Plus weekend master classes? She'll end up injured and burned out with that kind of schedule. Better to have her take regular dance classes (if she wants to) and re-evaluate for the competitive dance team next year, now that you know what it involves.
I would just tell them, when you spoke with the manager, you were told these 2 competition dates plus classes Tuesday/Thursday (or whatever), but that no mention was made of weekend classes too - and since you do not have full-time custody of her, and she has cheer and gymnastics, it's not going to work with her existing sports that she was already signed up for.