you need to pipe the satellite into the jukebox through auxiliary then use a blue DI box to go back into the receiver.
problem is, as you describe, it sounds like the satellite radio is internal to the receiver. you likely aren't going to be able to extract the audio to feed it into the juke. they often don't output those signals because it would allow recording. but if you did or it is enabled, you would also need an external amp to drive the speakers.
if this was a portable unit like an onyx, stratus, or starmate (like what you'd install to a car) this would be easy. Portable units can be had super cheap, (I see them in thrift shops for 10 or 20 bucks) see if your location would consider swapping to a portable unit if you bought it. they can call and just have them switch the account to the portable unit. There is a fee to switch radios that varies by what package you have. (I think if you have everything it's max 75 bucks. but it's less for just basic service.)
then it's just a matter of piping the portable output into the touchtunes computer input (use a red DI box if JCB or the adapter cable if MJS computer) and then feed the juke audio out through Blue DI box into the existing amp input you have already.
then they can just leave everything and the juke will switch everything.