Florida in the winter months gets crowded. You are going to have to preplan your trip and make reservations. Depending on the area you need to act immediately. For example, some of the most popular camping areas are in the Keys. People often book for the next year as they complete their stay.
I suggest starting your plans by deciding on the areas you want to visit such as the Everglades, Keys, inland lakes, etc. Searching Google maps for campgrounds in those areas would be my next step. If you are having trouble getting started, contact tourism departments for the State and local communities.
Kids, 4 bikes, 1 or more kyacks and a small truck camper... you are taking on a lot to start your TC experiences. I hope you are not also trying to take dogs or other pets.