I think the real question to ask is to whose bank account is this money going into when you swipe your card? Who is the adult that is monitoring the business of these kids since they aren't of legal age to even GIVE their information to a company on the internet, as stated by COPPA that was passed in 1998?
Children AREN'T responsible. I think if you went up to a child and said they charged you $1500 instead of $1.50, their face would light up with fear and they'd run off home and cry to their parents. They have absolutely no idea what to do in a situation other than that. It's not like they can call the bank up and deal with it themselves.
It would be a simple chargeback, but it would be one of those things that would completely freak them out, especially since they don't know yet how a bank account works at that age.
There's really nothing wrong with them using the Square reader, but there are other apps they can use to help figure out how many cups they sell/how much money they've made, and allow them to take cash instead.