I think the best thing to do is to rent out your own boat and go on a fishing trip. You can go deep sea fishing and also stop in the shallow water by all the islands on the coast of Belize. That way, the children can swim in the shallow water and you can go wherever you please. I have always enjoyed going out fishing with friends and it is a great way to have fun!!
With the fish you have caught, you can head down to Laughing Bird Key near Placentia. It is a small island about 100 ft long and 30 ft wide, shallow water all around with thousands of small birds and the fishing is excellent. You can get a guide to help you find it and it is a great place for a picnic, or a beach-b-que as margarita said. I hope you enjoy your trip and post up what you decided to do