Labadee is fabulous. Loved it.
I did snorkeling, zip line, and a tour (which I'd skip if I went to Labadee again). I walked around the whole place and there are lots of places to chill or play in the water or beach. There is a water park/playground kinda thing on a small scale that I'm sure kids would enjoy. There was also construction going on so they will have added things since I was there a year ago.
Lunch is provided on Labadee, which is very nice.
After I did all my excursions, I chilled in a hammock until the last tender left at 4:30 p.m. I so didn't want to leave.
I think you and your children will enjoy it.
As for kids' programs, I did see children in the children's area and I saw some kids doing a scavenger hunt. I was actually kinda jealous and wished they'd had a scavenger hunt for adults too. It seemed like they had plenty of activities to keep the kids occupied, but you could always ask RC ahead of time. Check out their site to see what they say on this subject.