Burl,
What about a wireless TV? I once bought some stuff from X10 to do that. My plan was to take a TV out to the back deck at home once in a while. Heck, I'll send the stuff to you if you PM me your address and pay the small shipping.
Now, I haven't thought it through, and maybe there is some reason it would not work on an RV system. But it should? I have the box here by my desk. "Audio/Video Sender & Receiver" model vk55A. Also a 5 in 1 universal remote. Not sure if that's necessary but I'd included it.
I don't see it on the x10.com website. Probably it is old tech, and won't do HDTV. I opened the box and see it uses RCA red/white/yellow cable connections on each end. So your antenna signal would have to be outputted some how to RCA and into the little sender box. Then at the TV you'd need the little receiver box, with RCA cables into your TV. Anyway, if you want it, it's yours. :)