Never been there but online info looks nice. My usual method for checking out campground is: allstays.com Here is the link to ALL Florida parks, zoom in to outside of bay near Tamps and you'll see the little "C" in a circle, hover over it and you'll see the park name, click for info and links
https://www.allstays.com/Campgrounds/Florida-campground-map.htm. It looks like the bath houses are close and convenient, there is water and electric at every site and there might be only two dump stations, one near the entrance and the second near the causeway connecting the two islands/keys.
Next I usually choose the RVparkreviews to see what people say. Keep in mind people camp differently so when I see a negative review that says nothing close by, I'm happy if all I want is a quiet place to camp. I just make sure we have everything we need on board before we go. Note the cell service comments. If you are trying to keep in touch with the family group, this might be important to you.
http://www.rvparkreviews.com/regions/florida/tierra-verde/fort-de-soto-campground. I also use Google maps to zoom in to the campground then change it to satellite view so I can see the tree cover, spacing between sites, etc. And last, I Googled "fort desoto campground pictures" and looked at images where I can see large, flat campsites, most with gorgeous water views.
You will have a long drive to anywhere but it looks like a beautiful place to stay. Enjoy!