First, you can split the OTA TV coax after it exits the 12V power supply (usually a wall plate with an on/off switch or button) and send that signal anywhere you please.
For satellite TV you cannot use a splitter but you could use an A/B switch. However, depending upon the how the coach is wired this may or may not be possible.
If you have a video control center where you are able to push a series of buttons to select what is viewed on TV1 and TV2 then the cable connection comes into the back of that box. Disconnect that coax from the back, connect to an A/B switch and feed one connection back into the box and the 2nd coax directly to your satellite receiver.
If you have a wall plate with the on/off switch and you select either watching OTA TV or cable by turning that on and off there is a good chance that you will be able to remove that wall plate, disconnect the coax connected to the Cable port, add and A/B switch and feed on coax back to that connection and the 2nd coax to your satellite receiver. There is a possibility that in this setup the manufacturer installed one or more splitters between the outside connection and this power supply. If that turns out to be the case, this will not work and your only option will be to run a new dedicated coax.