disneynutt is right on the money, if I may use such a pun.
There can only be one room charge account per room. You can't set up separate room charges for each card.
However, you can get printouts of your account as often as you like, and each transaction will include the number fo the card used to make the transaction. You'd have undisputable proof of who charged what and where and when it was done.
However, this gives each cardholder the potential to charge the entire amount that the room charge is set up for, so you are taking a slight risk there, depending on how you think your kids would handle such things.
And by the way, in setting up your room charge, you can back it up with credit card, debit card, travelers checks, cash, even Disney Dollars. Each level of resort has a maximum, and you can choose your own room charge limit to be any amount up to and including that maximum. That maximum is $500 at the Value Resorts, $1K at the Moderates and $1.5K at the Deluxes. Once the room charge has reached that max, your credit/debit card (if you used one) will be charged, and then you can immediately set up another room charge by phone (if you are, for example, at a park and not at your resort when you reach your limit).
If you use a credit or debit card to back up the room charge, there will be NO HOLD or charge placed on that credit/debit account. They will "run" the card just to make sure it is active, but there will be NO HOLD placed on it, and no amount will be charged to you until you reach your limit or you reach check-out time, whichever comes first.