I managed a fly fishing lodge on Ambergris Caye and got to visit a lot of other nice lodges.
My first choice for a family vacation would be Sleeping Giant Lodge. It offers a beautiful setting in the Mayan Mountains, great food and a lot of activities on the property or near by. They also have resorts on the coast so you can easily combine the rainforest with the Caribbean.
One of the most memorable outdoor things of my life was hiking to the top of a small peak on a misty morning to watch the sunrise while Howler Monkeys echoed through the valley and a pair of Scarlet Macaws flew by.
https://www.sleepinggiantbelize.comFor summer ocean and beach trips I would look at southern Belize, like Placencia, Punta Gorda and Hopkins, instead of the more popular northern San Pedro/Ambergris Caye. Sargassum weed now covers up the ocean side most of the summer causing dirty water and a sulphur rotten egg smell.
An unpleasant part of my job during Sargassum season was walking down to the dock to greet new guests and seeing the look on their faces as they stepped off the boat to see muddy water and our grounds crew shoveling piles of stinking, rotting seaweed into a front end loader instead of the crystal blue water and peaceful beachside setting they expected. Feel free to message me for other ideas, questions, etc.

Picture they don't put on the websites.