RV Camping with rental cabins available

lakeside campground, Aurora, KY, I thought had some rental units at one time. if not IIRC there is a bunch of cabins/campground just across the road and a little further south.
bumpy

Never been there, but my suggestion would be for Memphis, TN. It is about a 7 hr drive from Dallas and from Knoxville and about a 4 hr drive from Birmingham.

Looking online, there are several campgrounds with cabins.

Here is a state park that is 13 miles north of Memphis on the river.

Meeman Shelby State Park

I stayed in one in the Nashville area that was on a lake, just SE of town IIRC.
friends stayed in a cabin and we were in my MH.
bumpy

Village Creek State Park Arkansas in Wynne, AR.

Closer to Dallas but farther from Sevierville is Catherine's Landing RV Resort on Lake Catherine in Hot Springs. Lots to do in the area. Nice RV park with full hookups and either yurts or cottages to rent. Only certain cottages are pet friendly. We always stay here when we go to Hot Springs. http://www.rvcoutdoors.com/catherines-landing/

A lot of KOA campground have cabins also.

I did notice that the OP mentions "pet-friendly" cabins. As a rule, KOA does not permit pets in their cabins. As for other CGs, this is a policy that will probably need to be checked out individually with each CG. Perhaps, as a last resort, the pet(s) can stay with the part of the family who are camping, rather than at the cabins?

Did you consider Branson? We use Compton Ridge Campground & Lodge there. I know they have cabins and rooms that are pet friendly. Check their website, comptonridge.com