Royal Caribbean. We chose the ship (Harmony of the Seas) because it was one of the largest in the world and had the most different activities. From waterpark to climbing wall to a 10 story slide to everything else, there was always something for everyone to do. They seemed to enjoy having so many things available. They did spend a lot of time with kids their own ages in the special "clubs" run by the ship for each age group. We also chose an itinerary that included RC's private island, which IMO is the best of the private cruise line islands, with a lot to do and a huge water park.

We chose the Caribbean destination because I taught them all how to snorkel and wanted them to see the incredible creatures and things you can find under water. Hopefully it will spur a lifelong interest in snorkeling or diving. Our itinerary included Coco Cay (the private island), Honduras, Costa Maya, and Cozumel. Port activities we did included snorkeling, nature (sloths!), Mayan ruins, sightseeing, and cultural activities.

My grandkids ages were similar to yours, with one or two a little older. If I had it to do again, I'd almost certainly do the same. Hope you have a GREAT time.

As a bonus, we sailed from Port Canaveral and were able to spend a week at Universal Studios after the cruise. It was a huge hit. I have a lot of Harry Potter fans in the family.