The cable thing you're referring to on Haiti may be the zipline. I haven't done this specific zipline, but have done ziplines in the past, and enjoy them. I'll probably try to do it on my upcoming cruise in October.
Do your kids like snorkeling / swimming? If so, then I would recommend a Stingray City excursion in Grand Cayman, or maybe just a day at Seven Mile Beach.
In Cozumel, I have heard good things about Paradise Beach, which is another beach club, but no entry fee, as their impressions are you'll buy drinks / food when you're there, along with other stuff like their water activities.
Whatever you do in Jamaica I would highly recommend sticking with a ship excursion, as I have heard Jamaica is not the greatest of ports. Cruise lines have contracts with reputable tour operators, and you are on an escorted tour.
The only ports I've been to so far are Grand Cayman and Cozumel. It sounds like you're on a similar itinerary as me. I leave October 3 on Freedom of the Seas (Royal Caribbean).
2007 - Majesty of the Seas
2009 - Enchantment of the Seas
2010 - Freedom of the Seas