Your situation does sound very tricky indeed. The 11-year old girl sounds like she really needs help now...I can understand why you feel compelled to stay, despite your need to put your own needs first. You have been a big part of her life.
How old was the girl when she went to see that one T, who described her as having a "red" personality? I wonder if that T mentioned it to the 11-year old girl in that appointment. She's only 11-years old, waay too young to be considering personality disorders!

I wouldn't be real eager to go back into T if I were the 11-year old either. I would recommend trying to get the girl to try T with a different T, one who specializes in children.
I assume that you don't have much control, but I would think that the mother respects your opinions. So, having a serious discussion with her about how you're feeling would be helpful. She may not know how deeply this is bothering you ~ and doesn't want to lose you. Be honest, and hopefully, the mom will find a better match in T for her daughter. Gentle hugs and best wishes to you!