First of all, check out http://www.CaribbeanPortReviews.com
for tons of information about the ports you are considering.
In Grand Cayman, I would definitely suggest that you invest in Stingray City. You can do it off the ship for less money and a better experience. It is something your kids will remember for there entire lives and may well be the high point of the cruise for them.
In Ocho Rios, save the money here and simply head into Margaritaville. They have a pool, water slide and Jacuzzi, as well as a great beach. It won't cost you anything more than the cost of drinks and food if you decide to eat there and your kids will entertain themselves for hours. Use the money you save here to pay for Stingray City.
Mr. Sanchos will cost you $12 each way for a taxi plus whatever food and drink you purchae. Depending on which pier that you dock at, you might also consider just spending the day at the beach at the foot of the International pier. There is good snorkeling, shopping, food and drink and It won't cost you a thing.
Hope that helps.