I agree...
First, do they have cheer in school for free? or a community program that does not cost as much as at a gym?
Legally, you do not have to pay anymore than court ordered. You can choose to send her to a different one/less expensive or tell child that when she gets to X grade they have it at school. If you do pay then pay the place directly and keep receipts.
As kitty said, she can try and bring it back to court to get extra's split between you too. Maybe offer 50% and you will pay the place directly especially if the child really wants to do it and you can afford it.
As far as they saying anything about the other kids in the family, try just to ignore or one time you can say "you have all the money for
SD through the courts, it is your job to use the
child support money AND your share to get what she needs. If it is really an issue, then we can switch custody", but really ignore...