The only issue you could have is that the equipment isn't rated for installation in an RV. But I don't know what exceptions are made for demonstration purposes. Just wondering if you might have insurance issues if there was a fire.
You might want to have a button to remotely kill the gas flow...or mount the propane tank outside the trailer. You might be able ot get a solinoid tied to a smoke detector and/or have the solinoid from the tank only open if there is power to the furnace... then have an e-stop button or disconenct mounted outside the trailer to kill all power. Just a thought. Always best to be prepared for the worst case. Love the set-up though.