There are no AUDIO/VIDEO inputs on the DVD /radio that came with your GreyHack?
If not, there are ways to do, but it involves a spliter box for your speakers.
A switch would be for the DVD/radio output
B switch would be for the Satelite Receiver output. It's a pain to do it this way, but it's a cheaper way to make it work.
There are other ways to accomplish your idea so if you want to PM me, I go in to more details with a Audio/Video switch box, a distribution box or a new DVD/radio system.
HAPPY CAMPING!! :D
Daryl and Sandy
2013 Eagle 314BDS
2012 Ford F150 Platinum, 4 x 4 Crew Cab with Ecoboost
Equal-i-zer Hitch - Prodigy Brake Controller