boatdoc,
If your Bighorn is wired according to the Bighorn AV diagram on the factory website (image below), there is no splitter in the line between the UDC and the LR TV. There is an A/B switch which you can remove depending on how you plan to wire up the satellite receiver to the TV (RF, Composite, Component, HDMI etc.).
There is a splitter in the line that "comes from" the BR TV to the LR TV. Looks like this line carries the local antenna signals. The splitter is likely used as a combiner (wired in backwards on purpose) to combine the cable TV signal onto the same line.
If it is your intention to use the one cable between the BR and LR to send satellite signal from the LR to the BR, be aware that the wall plate in the BR will not pass the satellite signals. From the looks of the drawing, this wall plate contains the amplifier, power supply and splitter for the local antenna on the roof. You need to get that wall plate out of the circuit in order to pass satellite signals through it. A better bet is to not compromise the local antenna and wiring, rather, run a second, separate cable to the BR for satellite. Run it through the underbelly.
There are many, many ways to wire up a coach depending on what a person's needs are. For an RV manufacturer to know or to guess what everyone could possibly want or need, there would be an awfully lot of cabling added to the RV which would increase the cost by hundreds of dollars, certainly. And the sad part is that fewer than 50% of the owners would want or need it, yet everyone would pay for it.
Give us here a clear picture of what you want to do and we will tell you the simplest way to do it with the minimum amount of work to do it.
Sorry this is causing so much frustration for you.
Jim
//heartlandowners.org/attachments/BH_AV.jpg