We did the same cruise in June last year, but it was on the Fantasy. Of the 5 cruises we have done-this was 20x better than them all. Fawzma's tips are spot on and all I can add is
1. Don't miss any of the evening shows-they are almost Broadway standard. Aladdin was fantastic.
2. No casino on board (yay) - but bingo is a lot of fun.
3. When kids are in bed, the adult game shows in the night clubs are a riot. I'm not much of a night owl, but would often be there around 11pm onwards just for the laughs. The cocktails really help too.
4.Castaway Quays is a fanatic day of snorkeling and exclusive to Disney. Head toward the buoys you can see in the lagoon-there are sunken sculptures on the bottom.
5. Check what dress-up theme nights there are and take your costumes-fun for the kids to participate and makes you feel part of the community.
6. Meals rotate around the various restaurants and as said, you can ask for as many helpings as you want. The wait staff follow you each night so learn your preferences very quickly.
7. Our kids were 6,8 and 11 and had a ball at the clubs and the shows. The entertainment crew are so professional. Sign on the kids club as soon as you get in board-the queue get hectic really quickly if you wait.
8. If you want to do wine tasting, cocktail makeing and similar-go straight to the bars and sign up early again-these fill up really fast (and I highly recommend them).

Enjoy!