Eugene the kids won't be able to pay for their things in the shops aboard using the Disney Dollars. No money including Disney Dollars is ever exchanged in the stores. When you check-in at the port you are asked for a credit card. Your credit card is used to set up an account for those in your cruising party, or those you allow to charge to your onboard account, your stateroom key is used to charge everything on the ship. Now, you can let that credit card ride to pay off your account at the end of cruise or you can pay off your account with cash or if you have enough, Disney Dollars.
What you could do is call Disney or Magical Treasures what ever they are calling themselves now and purchase on board credits for them in their names. A gift card will be waiting for them when they arrive to their stateroom, I should say it usually is there waiting, if not the stateroom host will deliver it. You can call them 1-800-601-8455 they start at $25. and go up. The amount of the GC is automatically credited to their stateroom account.
Correction: it's now called Gifts Ahoy! the phone number is the same as I stated above.