I search at the vacationstogo.com website, but they require that you register with an email. I'm seeing only two 7-day cruises departing from Galveston just before Christmas: a 4.5-star Carnival ship, that calls at Jamaica, Grand Cayman, and Cozumel; or a 5.0-star Royal Caribbean ship that calls at Roatan, Honduras; Costa Maya, Mexico; and Cozumel. So if you must have Jamaica in the itinerary, it's the Carnival cruise or nothing.
Are you looking to get two cabins, with one adult and one child in each, or all four of you in one cabin?
Good luck!