I don't actually see what this discussion is about.
Surely if you as your daughter's Mum don't feel that the gym classes are safe, it is your responsibiity to stop your daughter attending until there is someone in place to supervise properly.
I glean from what you say that your kid has some natural ability, but how would you feel if some other child got injured as a result of lack of training or supervision and you hadn't said anything?