N.W.
I'd say your daughter is too young for the daycare at the gym. I agree, those workers aren't usually trained day care workers and they don't run good "control" on the kids. At a real day care center they'd address the problem, perhaps a time-out and then watch the kid closely so they didn't do it again.
Your child is "normal" because hitting is a phase most kids go through. At a regular day care center they'd work with you on a plan to handle it (we always did) but at a fitness center where you essentially get a "sheep herder" for two hours they are not going to bother.
If it makes you feel any better my husband used to drop his daughter off at daycare at the fitness center where he worked (free day care). She always came out all wild, usually with some kind of injury. The workers were untrained teenagers who just sat in a corner and gabbed with one another. He stopped taking her there after a while.
Good luck! Perhaps you can try again after she gets through her hitting phase.