Some of the Dish Receivers can be viewed by two different TVs simultaneously and independently. For example I have a 622 and also a 722K. Either can be viewed on two TVs independently and simultaneously. (The resolution on one of the TVs will be limited to SD via Coax from the receiver.)
Each of those receivers has two Satellite Tuners that can simultaneously record and the 622 has one OTA Tuner and the 722K has TWO OTA tuners.
So, on my 722K I can record potentially four different stations and simultaneously view a previously recorded event.
I have no experience at all with RVs, so I don't know what Antenna issues you might have. My 722K and 622 each have one coax feed from an Eastern Arc rooftop antenna at my residence.