This is what I was wondering, have you talked to the parents and if so was anything done?
I think bringing this up to the current coach is tricky.
Rather than being specific, could you say something like “I don’t know if my daughter ever mentioned this to you, but she was bullied by other girls at her previous gym. The bullying was in person and online. This situation became very toxic and is a major reason why she switched gyms. I am concerned because I have heard through the grapevine that the two girls who bullied my daughter may be looking for a new gym and may come here. Can you tell me about your gym’s behavior policy (in person and online) and how you will handle a situation like this if it comes up?”
In other words, no names, nothing in writing (which could get passed around) or offers of proof, which would involve showing them online messages written by others, and try not to give the impression you are asking then to not take on these girls. If the coach wants more information then they can ask and you can decide at that point whether to provide it. In other words, it’s more on them at that point what info is shared.
The reason I suggest the above is because I would be concerned about avoiding looking like the bad guy here, which could happen if it looks like you are telling tales about other people’s kids to prospective gyms (even if those kids are bullies.) I also think that a gym- especially one in the middle of an expansion of their program- is unlikely to refuse to train a kid because of this kind of behavior in the past at a different gym. What is most important is how they would handle this type of behavior should it occur at this gym.
Having gone through bullying at the gym of my eldest (a boy) there is no easy solution. As frustrating as it was, what helped the most was helping my son put this behavior into perspective. Happy, secure and successful people don’t need to bully others.