If the entire balance was paid to AAA for the room, then you won't have to worry about having the card. However, if it was only the reservation thru AAA and you have to pay when you get there, you may be required to show the card.
If she got you a Disney package thru AAA, then you won't have to show the card. Everything is handled by AAA and you just have to do the checkout to cover any room charges.
HTH