Coupled with the fact the water is a tad chillier at that time of year than the islands further down the chain in the Caribbean, or at least we thought so the year we were there at Christmas, and the breezes were stronger, too, so when you put them both together, I don't know if it would be the best choice for a family water-based Christmas trip. A wonderful place for sure.
I'm thinking anywhere you travel during that time of year the costs will be way up there.
Have you considered Turks and Caicos? I haven't been there myself but my daughter and her family were there around the Christmas holidays and they all loved it - the parents and the kids - twenty-something and a teen-ager. Just another possibility....
"Always keep your words soft and sweet, just in case you have to eat