One of those 3 coax connections (probably the living room) is probably on the Winegard antenna amplifier control. It has a little black push button and light in addition to the coax connection. This control has two inputs (OTA antenna and "Cable-TV" In) (as well as 12v power). It has two outputs: One you see on the front and the other on the back is what is driving that splitter for TV in the other two rooms. If your Sat receiver has "coax out", you can just connect that to the "Cable-In" on the controller and you're all set. (If your RV has a cable-in on the outside, you could put an AB switch to select that external cable-in or the Sat out.)
Note that turning that controller on (light) gets OTA distributed throughout your RV. When it's off, "Cable-In" is distributed.