I haven't been to Belize nor Roatan so I'm sorry I can't help you there.
As for Grand Cayman, my daughter was about 5 when we went on the Atlantis semi-sub excursion there. She really liked seeing all the great fish up close. The semi-sub is good for kids because you can always walk to the top for a breath of fresh air if they don't like being below the water surface. Also, Seven Mile Beach is from family friendly and can be easily reached by cab.
As for Cozumel, one time when my daughter was about six years old, we went on a Folkloric Show excursion that had lots of frilly Mexican costumes/dresses, which she enjoyed. Also, see my article "Back to the Beach" for recommendations on beaches in Cozumel, along with other Caribbean/Bahamas destinations.
I hope this helps. I'd love to hear about your cruise upon your return!
Luisa Frey Gaynor