There may well be two separate cables from the head unit (in the dash) or a Y of some sort. These are most likely composite video runs, with separate audio cables. It's a separate cable system from the RF coax from the antenna, of course, as you presumably realize since the broadcast TV is lovely everywhere.
The head unit is typically removed by pulling off any trim ring or trim plugs and then sliding some sort of a thin metal key/tool in slots in either side of the radio (to disengage the catches that hold it into the dash mount) and then sliding it forward. The precise details of where the tools are inserted and what shape they are and so forth vary from radio to radio. If you have a manual for the radio, it might tell you more details. (If you're fortunate, the sheet metal keys were included with your RV somewhere and nobody has thrown them out not knowing what they were.)
I've no idea how your particular TV is mounted. There are a wide variety of mounts possible.
My guess is that there is a poor connection on one of the video cables, and probably unplugging and cleaning and replugging them will cure the problem. It might be necessary to pinch the outer shell of the RCA plug slightly to get good contact there with its socket. A bad cable is certainly possible, but in my limited experience poor connections are more common.