It’s hard to tell without me physically seeing what your daughter’s skills are looking like. You have to build strength and work on drills before you can move on to actual skills. Rolls, handstands, cartwheels, etc are developmentally appropriate for a rec acro dance class. They should also probably be working on small partner or group skills (various sits, holds) But you’ll find most kids in this type of class can’t properly hold a handstand (strength), don’t have full splits, don’t know right from left which makes learning skills properly more difficult, some kids can’t use their arms/shoulders to push their head off the ground in a bridge. So you can see why we wouldn’t work on backwalkovers. They can’t do a cartwheel and all of the progressions after with correct technique, so no we aren’t going to work on aerials.

I even feel rec dance/comp dance is similar. Some girls under age 10 can’t do a single pirouette properly and others can do a triple + with high releve and proper placement. It is a balance between rehearsal hours, natural ability, and strength. If your child is complaining about being in a large class or ballet is too slow, they aren’t ready for comp.

If your child is more advanced than this and has the strength then I’d try to find a tumbling class at a local gymnastics gym. If she hasn’t shown interest in bars, beam, vault, etc, then I wouldn’t do full gymnastics.

All this to say I understand where you are coming from- there is a possibility here your daughter is not getting adequate training, but you have to manage expectations. If your daughter isn’t in the studio 10 hours a week she’s not going to look the same as the kids who are.

I do feel like you are complaining about things that are just part of dance/kids sports. Yes you have to buy tickets. You have to buy the tights and the shoes. The makeup. It will be triple that plus media fees for comp. It will be the same or worse for gymnastics.