That sounds like a good story from a guy who really doesn't care to find out!!!
So we learn to do it ourself, huh?
So is this the drawing you have looked at?
https://www.winnebagoind.com/diagram/2017/000182321.pdf
Looking at page three lower end, I see an HDMI connection (located above radio?) and looks like there should be an HDMI cable off the rear of that going to a splitter. One lead off the splitter goes to a TV and the other to the bedroom TV?
So if Dish is plugged to the connection /HDMI wall plate, it doesn't come out both at the front and bedroom TV?
Or am I just missing communitactions with what you are seeing? This communications stuff is harder than it might seem!!
If you need to get to the splitter, I might pull the cover and tug on the wiring a bit to see if it is not located just a short distance away. Splitters I've seen in RV are sometimes not even attached but just hanging on the coax and might assume the same for HDMI....
ASSUME can get us in trouble but sometimes it's the best we get.