Both Dish and DirecTV use coax connections between the antenna/dish and the receiver, even for HD. DirecTV needs an additional 12v wire to aim the antenna, Dish supplies the aiming through the single coax.
From the receiver, you can use coax or HDMI cables from the receiver to the TV. If you have a newer flat screen TV, then HDMI would give you the best signal and you will have a sharper picture. If you have one of those older tube TV's, then you will be stuck using coax from the receiver to the TV.
Then your challenge comes with handling the TV in the bedroom. If you want the satellite signal to go back to the bedroom you are looking at a whole new set of different problems, and the solutions could be many.
I am just contented with satellite on the main TV and OTA on the bedroom TV.
I just looked at your wiring diagram. With the video switch box, you will not get HD signals to the TV. I ran into this exact problem with my last coach. To get the best picture, I ran an HDMI cable directly from the receiver to the TV, bypassing the video switch box. Then, I plugged the HDMI cable into the HDMI port on the TV. Then, using the "source" function on your remote, I could switch back & forth between the video switch box with it's coax input and HDMI. The only problem was that I had to use the TV's speakers with the HDMI, which, thank goodness, wasn't that bad.
Out West Somewhere
2016 Sunseeker 3050DS towing 2006 Hummer H3