You may want to contact Disney to be sure they are accepted. Many places around where I live no longer accept them (even though they have Visa or MC on them). They also have to be processed differently than a regular credit card. Your kids will have to keep track of the balance as the exact amount has to be entered in to the machine. They have to know there is more ( or the exact amount ) is left on the card. For instance, if the total is $10.00 and the amount left on the card is $5.00, the cashier has to enter the sale as $5.00 then do another transaction for the balance or the card will be declined. It doesn't seem to work automatically.
My recommendation would be to give them Disney Gift Cards and keep some cash on hand for the few vendors that can't take cards ( some of the carts only take cash).