Besides the basics....
1. Extension cord, cabins only have one plug, with cell phones, camera and tablet or lap top you need more then just one plug. Some cruise lines do not allow power strips so an extension cord with 3 or 4 outlets is good to pack and it can roll up in one of your packed shoes so does not take up much room.
2. OTC meds. They are very expensive on the ship, sea sick bands, Pepto, Advil, tums, small sizes of that kind of stuff. Maybe also if the kids have a favorite hard candy as a treat (or treat for the adults)
3. Antiseptic wipes and hand sanitize. I also wipe down the door nobs, light switches, TV remote, drawer pulls and flat surfaces that I will touch.
I would also suggest
A night light or battery opp led light in the cabin or bathroom, the bathroom light at night can be blinding. Some canned drinks (carnival does not allow plastic bottles to go onto the ship) for in the room in case kids want some at night along with some crackers or munchies for the kids night time snack.
Pack a carry one bag with swim trunks and pool gear so you can start enjoying your first day before your luggage is delivered to your cabin.
Some ships do have self serve laundry, so you do not need to pack as much, if somethign gets dirty you can wash it.
Have a great safe time and create memories of the kids first cruise.