Seems to Me that most Satelite systems have several output options! On Ours the HDMI output goes directly to the Front tV. The secondary Y R W goes to an RF Converter and on to the existing RG60 Cable and the rear Bedroom TV. There is also sometimes a regular RG59/60 output which in Our case runs to the Basement TV.
All work at the same time with No Splitters or Push Button Switch Boxes, although those could certainly be used.
BTW We have two sat receivers connected at any given time that are both functional and usable at any of the three locations at the press of a button on the Remote!