Good points. If you’re feeling that strong of a toxicity there, tell her it’s either switch gyms or do school activities. Point out to her specific examples of negative lessons you think she’s learning there. Maybe if she has a more-detailed understanding of your concerns, she’ll be more willing to leave (or at least not call you “mean” for yanking her from her friends lol).
Being shy in new places is a good thing to get used to, good practice for college and beyond. I’d explain to her that there’s always going to be a point where you have to leave current friends and find new ones; and making new friends usually isn’t that scary at any gym. There are usually a few quieter kids on every team, and they may to gravitate towards each other. Also, the larger the gym, the more likely there will be other new kids on your daughter’s team too, so no worries about being shy and feeling out of place.
I’d just encourage her to go to the Tryout (or a Tryout clinic right before). A private gym visit or Open Gym where you’re forced to interact with people right away or stick out as “the new kid” might be too intimidating for a shy person. At least at a Tryout at a larger gym, there will be many other new kids there too and they can all be shy together lol. No need to really talk to anyone at a Tryout, you can just focus on what the coaches tell you. And then you end up making new friends naturally based on where the coaches place you in a stunt group, etc.
If she already has Level 5 potential or may be there eventually, I wouldn’t automatically write off her ability to end up on a Worlds team within 3 years. Sometimes being at a larger gym that cares more about growing an athlete’s skills to reach Level 6 will help her progress more easily. And if tumbling’s the issue, there tend to be a few non-tumblers on most Worlds teams. Athletes sometimes end up on Level 6 not solely because they’re the most talented, but because of intangibles (positive team player, very hard working) or because they fill a role well (very tall for backspotting, etc). If she likes following Worlds teams or wouldn’t mind being on a team like that one day, I’d definitely mention it as a perk of being at a larger gym.
Most large gyms tend to have some strong teams in Levels 1-5 too because of how large their talent pool is (there are a couple exceptions where a Large gym is blatantly not well-rounded in Levels 1-6, but for the most part, you can’t go wrong). Maybe look on VarsityTV for a video of a strong team at the new gym and watch it together and point out how good they are.
I’ve never heard of a mandatory graded school function at night. That’s crazy of a school to require that when every kid/parent has different obligations after normal school hours. I’m thinking most gyms may have given you a hard time on that one. But I totally understand your overall concerns.