We recently cruised with our DS, who was 21 months at the time. The nursery was awesome! They were very accomodating and so gentle and loving with our DS. It was also the first time we had left him with anyone other than family, so mama was a bit unsure!!
I'm not sure about your daughter being able to stay...you can ask them. But you can stay with him as long as you need, and they also have family time...which is during the time they are not actually babysitting. Parents can come in with their kids and play. This may help him become comfortable with the area. My DS just walked away from us the first time we left him...no looking back! I was a bit surprised, but happy that he was OK with it. We also stopped back and watched him through the two way mirror, and he was really enjoying himself. They have lots of toys and of course Disney movies, to keep the kiddos occupied.
If you want, try to change your seating when you get on the ship. Usually this is not a problem. They have a place for dining reservations and changes that will open soon after boarding starts. Get there early and you should be able to change your dining time. We did this so our DS could join us a couple of nights, and then we went to Palo one night and took him to the nursery.
As for the rest of the cruise...he loved it! Just walking around the ship and looking out the windows could keep him happy. The PP was right about naps, make sure you make time for this. It really makes things easier, even though it can be a hassle. We would have our DS nap on the bed, and close the curtains. That way we could still watch TV, keep the lights on, etc.
Bring a few sand/water toys for the beach and also to play with in the ear of the Mickey pool where the little ones are allowed. And my son loved all of the deck parties...like the sail away party. He loves music and dancing.

If you have any other questions, LMK. We had so much fun, we are going again next month.
