I just had to jump in with a pep talk/advice? about choosing another gym, and a reality check.
The reality is that gyms are run like you parent your child. You have expectations, values, hopes, and fears that direct how you raise your child, while the kid down the street has a very different set of parents with their own expectations. Some families are vegetarian, others others have a mixed diet, and others subsist on take out and McD's...... all for their own reason stemming from values that work for them. I feel the same can be said about gym clubs, as they each seem to have values that suit them for reasons that suit them.
So which family is getting it right, and which gym is getting it right? For myself, my answer is any of them that has a constructive spirit that guides them to do what they do the way they have chosen to do it. In the context of 100 kids with varying goals, fitness levels, and sense of purpose, it's impractical to operate a gym club that can suit every child. There are just too many nooks and crannies that would need a team group, coach, and equipment time.
The bottom line, as a parent, is you have to go out into the community and shop for the gym that works best for your child now, and a distant future that may, or not, come to pass. This is a pretty important process because, even if your dd is not too old now, she'll likely get too old if she moves a few times to a gym that fits for a few years but fails to serve up the goods the third year. Ya see, she won't get from her point A to her point B if she has to lose a year here, and a year there. So shop well in the hopes it's the last time you need to do so.
Another reality check....... From what you're saying she want's to eat, breathe, sleep and dream gymnastics..... but you qualify that with the observation she's only 8, so, quite agreeably, who knows. The burden is, no matter what you know and when you know it, you have to be willing to travel down that same road and match her stride for stride....... so are you ready for that, or are you just going to cross that bridge when you come to it.
Really, a lot of what I've brought up is rhetorical, and meant to provoke some thoughts beyond wanting to provide for your child right now, as the actions you take in the next few weeks may hold sway over you in the future.
You've gotten some pretty good advice on this thread about switching and what to look for, and I'm sure you'll get further help if you ask for it.
Good luck to both you and your dear daughter.