I hope you did not sign a contract or make any commitments, as there are BETTER avenues for a 4 year old girl. There are very many serious schools out there that are just as capable, if not more capable of teaching children in a safe, controlled environment where they will additionally learn something useful.
2nd, forget about the MMA there. That's what they're calling it because MMA is the buzzword fad of this era to get people to sign on for class. Anything you learn there will be taught by people who DO NOT know what they are doing. You know this already because you know that they do not actually pinch or kick each other.
My suggestion of judo seems to be right out because I looked into it and there is no active judo club in your area.
Personally, if I were you, if you are determined to do TKD, go to the other school in Erie. At least there, they teach the competitive sport style as well and you might get some sense of distance and timing.
It looks likes there are a number of other non specified martial arts schools. You should visit all of them, at least twice each, on different class nights. Then make your decision. If you're taking this as seriously as you say you are, then you should take the time to make the right decision, not the most convenient one.