Yes, the KTTW card is your room key, i.d. and charge card. You will need it to get on and off the ship at the ports of call. (adults also need photo id). You will want to carry it with you as you will need it not only to get into your room but for any charges you may want to make (cash is not accepted on the ship, except for tips).
As for children, they will need their KTTW card to get on and off the ship and to get into the room. They will also have charging privileges unless you go to Guest services and get these withdrawn.
Whether they carry their own card depends on how old they are and whether they are going to have some independence from you on the ship. My kids are older so carried their own cards.
Having said that, when we were getting off for excursions or going around the ship, I seemed to be the person who carried all the cards!!
You can get lanyards to make it easier to carry the cards.
A word of warning - don't store the KTTW card next to a credit card or ship arcade card as this can cause the KTTW card to demagnitise so it doesn't work.
Hope this helps.