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Royal Caribbean are brilliant for children ( not sure about "kids" though).... Neil's son Fala.
WE have sailed twice with princess cruises ( Sea Princess) and the kids facilities are excellent, our son is now 6 but went at 4@5 years old.
They have loads of activities in the kids clubs and if you want some evenings to yourself to eat dinner in peace, you can have an early dinner with your child then put him/her into the club for a couple of hours and pick them up at 10pm, they tend to settle them down on bean bags to watch a movie and if they drop off to sleep you can then carry them down to the cabin or even take them to the show. We found it ideal and no problem. In fact the kids had a fantastic holiday ever.