Put thirty-nine teenage girls in two small dressing rooms and I will bet you even money that at least one of them will be in tears before the night is out. And that she will end up in mom's arms sobbing that someone is just a b*tch, or that the girls are so mean. I know this because I've been that mom.
But here's the hard truth, mom. You cannot do anything about this, and neither can anyone else. I know this because I've also been the coach that the mom comes to, asking me to intervene. To make the girls include everyone, to find her daughter friends.
A rink or a club or a school can make all the inclusivity rules they want (my kid's grade school had the rule "if you invite half the class, you have to invite the whole class" for instance, although the high school kids were on their own), but they cannot actually make the other kids talk to your child, and they cannot control what the kids arrange on their own time outside the purview of the program.
But there is something you can do. You can encourage your daughter (I don't know if this happens with boys-- anyone?) to stand up for herself. Shy children are sometimes perceived as stuck up or even mean. They need to reach inside themselves and find a way to be included that doesn't violate their own sense of self. If your daughter has been left out of Secret Santa, she needs to go to the most popular girl in the room and for heaven's sake just tell her "I feel so bad I didn't know you were doing this, and I did not get a present for anyone. Is there someone who got left out?"
Because contrary to the popular culture trope of "mean girls," the thing about the popular girls is they want everyone to love them, including the geeks, the unattractive, the shy and the stuck up ones. Popular girls are equality opportunity goddesses. Appear to worship her, acknowledge her primacy, and she's yours. If they think they've left someone out of their magic circle, they'll do what they can to include them, for the adoration alone.
But mom, you cannot do this. Your daughter has to do it. You can tell her what to do, but she has to take that step. You can't fix this. I can't fix this. Your daughter isn't 6 anymore.
The good news is, she won't be 14 forever either.
*(If your daughter has actually been mean and has been left out for that reason, or because you have antagonized everyone yourself, the two of you need to face up to that and change your behavior. Just saying.)