M.B.
It totally sounds like she started it because she's noticing that if she does that then you will soon have to be there. She wants you there with her and that is that. In a different situation I'd suggest not going to get her and let her deal with it, but the gym daycare isn't the place to do that... Maybe you could bring a friend along that could be with your daughter if she screams for the next couple times, so that the gym daycare people don't have to deal with a screaming child alone, but also your daughter learns that it is not the way to get what she wants.
Also, you sound very practical and may already do this, but I'd make sure if I were you to not let her get her way at all when she is acting like that (outside of the gym). To teach her that GOOD behavior is what gets her results...
Hope this is helpful
Rebecca