Do you reason that a gymnastics gym would transport a credit card for a expense on my little girls monthly fees?

Many of them will these days. The merely way to know for sure is to call the gym and ask them.

this would all depend on what gym this is. most places today are taking credit cards, however every place is different, you would hold to call them to know 100% for sure.

Answers:
It is entirely up to the individual business. They usually make it quite clear when you sign up. Without the nickname of the business, any answer you get is worth what you paid me for it. NOTE: you can't contact me though Credit12345.com and I did not provide any other way to pay me.

My goddaugher's doesn't, but some do, give the name them.

Ask them if they accept payment by credit card. If you want to remain anonymous, ask a friend or relative to call them and ask the question.