This is actually exactly what we have done - we have a tailgater, which we hook to the "cable" coax in the rear compartment.
Inside, in the cabinet over the passenger seat is where our satellite receiver is - and the HDMI output goes to a transmitter there, with the receiver plugged into the TV (we actually have 2 transmitters with a HDMI splitter, and a receiver for each TV, main & bedroom, because the one we bought can't link to 2 receivers)
We originally had one and just moved the receiver between the main TV and the bedroom, because we didn't watch them separately. with the HDMI splitter, you do have to watch the same show on both TV's however.
This is the transmitter/receiver we used.
works well, most of the time- we do end up with a sound mismatch occasionally, but it usually corrects itself after a few minutes.
Let me know if you have more questions.