If traveling I second the idea of a motorhome. If camping in one spot, find a local rental company and have them spot the TT for you.
I have never heard of any of the typically car rental companies allowing towing with their vehicles. Even if they did it would need to be equipped with an appropriate class receiver, brake controller and you would need a weight distribution hitch. The hitch especially takes tweaking to get it right...IMO more work than it would be worth.
Also, might be worth checking Craigslist, in my area there are a few folks who own Class A MH and rent them privately.