I have reviewed tubing down the White River on this site previously (this is the river tubing from Ocho). Our daughter did it when she was 8 and she is an extremely tiny person. You do have a life jacket. There is only enough "rapids" to make you feel like you have had a little adventure. The tubes have a metal bottom on them so that you don't "bump" in the shallow water and you would be pretty hard pressed to tip out of one. The scenery is beautiful. The guides, like so many people in Jamaica (not sellers!) are personable, talkative and happy in their work and seemed to like people in general and my kids in particular. My tiny daughter had a guide to herself who made sure she never got hung up on the banks. It was a wonderful time. Take a waterproof camera. One our favorite tours.
We did tube on the Great River (I think that is what is was called) out of Mo-Bay.
The water in March was extremely low. It was not as scenic and not particularly fun or worth it. Hope this helps.
Other things we have done with children in Jamaica is climb Dunns River Falls and tour a private estate garden (you make a human chain at the falls, it was okay with kids but I like the tubing better), horseback ride on a plantation and the beach (this through Shoretrips.com) which is our favorite thing we have done there.
I do not advocate going it alone in Jamaica, even for a short shopping trip. Stick with a ship's tour or Shoretrips.com (they are USA based, and insured, and haven't had anyone miss a ship in 8 years). Jamaica is pathetically poor with about 30% unemployment and a very high crime rate. Culturally the people trying to sell you stuff (give you a tour, braid your hair) are the most aggressive merchants I have ever encountered and many veteran cruisers stay on the ship rather than deal with them.
RCCL Nordic Empress 1993
RCCL Nordic Prince 1994
RCCL Explorer 2003, 2005
RCCL Navigator, 2004, 2007
RCCL Mariner 2006
RCCL Liberty 2008
RCCL Adventure 2009
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