St. Louis to Destin

If you go back through Memphis, there is a Jellystone Park. http://www.memphisjellystone.com/

It's a doable drive but a long one going down without a stopover. I do it from Kentucky once or twice a year. May I suggest rv park reviews online that will give you travelers' opinions of the parks and their amenities on your route so you can make the best choice for your trip. Good luck.

If you're taking 55 to Jackson, Ms then over to Hattiesburg, Mobile, etc and returning the same way, there's a nice COE park Just south on Hernando MS, which is just south of Memphis on Arkabutla Lake called Hernando Point. http://www.recreation.gov/camping/Hernando_Point/r/campgroundDetails.do?contractCode=NRSO&parkId=73201&topTabIndex=Search. Hopefully this link will work. Not a Jellystone, but a nice quiet park, at least when we were there in April. And Tunica isn't far if the Adults want to play.
HTH

Take a look at Rickwoods caverns state park. It is just north of Birmingham, AL nice park. We stayed over night on our way back from that part of Florida. I have notes about the sites.

That covers a lot of territory. Maybe you could tell us which route you intend to drive?

When I was planning our Tallahassee to St. Louis trip we were planning on staying at 1 Tranquility Base, Huntsville, AL 35805. However we found out that the Jehovah's Witnesses were having a convention and decided on on a differ route and stayed at the Holiday Travel park in Chatanooga, TN. (http://www.chattacamp.com/)