We always use either the pre-paid Amex travel card or the pre-paid MC travel card from
AAA. We have used them in the gift shops, the restaurants and even the carts that take cc. They are similar to the gift cards as they are pre-paid MCs and Amex's.
We have never had a problem using them anywhere in the parks, City Walk or the resorts. Never had a fee either.
The only thing you can't do is use them at check-in for your hotels. For that, they want a regular card. Although you can use them to check-out.
However, I am betting you are not planning on having your daughters use the gift cards for the hotels
Your daughters should be fine with the gift cards.