I don't normally do recommendations but I’m on a roll, having recommended Castara Retreats to two friends, one with a family with children the same age as yours, both came home saying it was" the best holiday they’d had ever had"
Castara Retreats isn't a hotel, but a set of apartments, one two bedroomed, two studio and one separate with one bedroom. Rainforest is ideal for a family, or failing that the two studio apartments are connected via the balcony by a door which can be opened. I have stayed in most of the accommodation so far and have loved it all. It can all be booked for 4 days or over from Sue and Steve a very helpful friendly British couple, on http://www.castara-retreats.com
The accommodation is self catering, but if you don’t want to cook there are places to eat in the village, or if that’s too much for you, you can get Duck to cook for you (he cooks like an angel). Porridge and Jeanell look after the visitors fantastically. They can recommend or arrange transport, trips out, car hire, or anything you might need.
Castara is on the Carribean coast, and has its own coral reef all the way up to the little beach, so a daily swim with the fishes is no problem. And everyone in the village is so friendly
My friends with children the same age as yours did the whole trip at on the lower end of your budget, this included boat trips, fishing trips, guided rain forest walks, and for the days they needed it, they hired Porridge’s Jeep.
They flew with Exel from Gatwick - a bit of a trek for you but the flights are half the price of most other companies
Hope you have a fantastic time