One thing I would avoid on your route is Louisville I-64/I-65. The Kennedy bridge is being worked on and traffic flow is SSSLLLOOOWWW. I live north of Louisville and will be leaving Friday also for Pigeon Forge,Tn., so I will go to Cinci then I-75 south. We haven't been to Charleston in 42 years so no help there. Have a safe trip.
If we were making that trip our first stop would be Nashville, 300+ miles. The next overnight would be Asheville, NC (280+ miles) with a tour of Biltmore. And then finally Charleston, SC, 280+ miles. You can check RV park reviews for campgrounds in those locations. In Charleston we have used the Mt Pleasant KOA with good experiences twice.
2011 HH DA 349 RSB 5th
2011 F350 Lariat 6.7L PSD CC SB 4X4
18K PullRite SuperGlide & 50 gal Titan fuel tank
Slightly out of your way, but very beautiful is Vogel SP in GA. Vogel is a very popular park and can be hard to get a spot, best to check before going. Close by is the tourist trapish town of Helen. A Swiss styled village worth the visit.
Camping in a Sportsmobile. How much better can it get?