If the camp fees are for your daughter, I don't think that it matters whether they are in the mothers name or grandmothers name. The grandmother is permitted to pay for camp fees for your daughter if she is inclined to do that for her owm daughter, but that doesnt mean that you are not obligated for your half of the expense.
I agree with Ms. Tebano. You are responsible for your daughter's camp fees if the order says you are. It doesn't matter whose name the bill comes in or who else might choose to pay the other parent's share.
This anawer is not intended to create an attorney-client relationship and may be considered attorney advertising. This answer should not supplant advice received from any attorney the questioner may have or obtain, as that attorney will be able to provide more thorough and informed advice.
If you are required by written Agreement or a Court decission, to pay for camp then it doesn't matter who the bill is sent to. Call the camp and have them fax you a copy of the bill. Visit the camp and see if it is a place you want your kid to go. Get involved.
One needs to analyze the agreement - assuming this was done pursuant to an agreement versus mere order. In addition to you, does it specifically require the mother to pay her portion? That said, I doubt it will actually have consequence as to who's paying the bill on her end. In any event, I encourage you to schedule a follow-up consultation with a Westchester Child Support lawyer.
* If you found my answer to be helpful, or the "best answer," please feel free to mark it accordingly.