There is a, "Disney Gift Card," App on the iOS App Store. It is quite good at tracking gift card use, and card balances are updated very quickly after purchases are made.
However, I'm nearly certain that the app's data is tied to a single device. I've never tried to enter the same card on two different devices, but I don't see why you wouldn't be able to. It could take a little time to enter each card on multiple devices.