iTunes one account with multiple users
Gift cards are tied to iTunes accounts so if you want to let the store keep track of the different gift cards you will at least have to set up individual iTunes accounts for each of them (and yourself). Of course this also means that you have to switch the user in iTunes accordingly each time you want to make a purchase.

Thinking ahead, this approach is somewhat future-proof as well. In a few years your kids will switch to their own computer account with their individual iTunes installation etc. If they already have an individual iTunes account as well they can keep using their apps without having to bother you in case of upgrades etc.