KOA and Good Sam private campgrounds for the pool, family activities, wifi (but really best to supply your own, for example your phone hot spot), full hook-ups.
Then visit (drive in) nearby state parks for the hiking and wildlife stuff.
We purchase the Indiana DNR season pass which gives us access into the Indiana State Parks and Recreation areas with no additional costs. Camping, of course has it's own fees. But if we are in a private campground, we can always visit a nearby state park or recreation area. Several state parks in Indiana offer horseback riding and almost all of them have trails and nature walks.
I doubt you find everything on your list at very many single locations, if any at all.