Hi C.-
I don't know your family but I certainly wouldn't think anything of it if it was my 13 year old cousin that wasn't coming to my wedding. Certainly if she had been a bridesmaid or had another role to play in the ceremony it would have caused a problem, but if she was only to be a guest at the wedding I don't understand why they would be mad, disappointed perhaps, but I would hope they would understand.
I guess the only suggestion I have for you is to call the cousin directly to let him/her know that your daughter is sorry she won't be able to make it but she has a commitment to her team. If you feel that the cousin will be understanding maybe even have your daughter call him/her so that she can express how difficult a decision is was and that she is sorry that she will miss the wedding. As far as the rest of the family goes, I wouldn't make a big deal out of it. If you need to let them know she won't be there then do so but otherwise I guess I don't think a big announcement is necessary.
Your family must be really close. Honestly if I was in a similar situation not only would my daughter miss the wedding to go play in the tournament, I would probably miss the wedding to go watch my daughter play in the state finals instead.
Sorry I wasn't able to be more helpful....
Good Luck,
K.