I'm new to all this but I think here's what my plan is.
I have an A126 Rockwood popup hardside. 3-way Dometic fridge (no freezer).
I plan on precooling on 120vac day before heading out, stock the fridge before leaving.
Then while on the road I'll use 12vdc to power the fridge. The trailer gets 12vdc supply form the Jeep through the 7-way.
Shore power at the CG will be back over to 120vac.
I can only see using LP when no shore power is available (boondocking).
From what I can tell my Rockwood A126 has a battery isolator so I won't drain my TV battery while stopped for short periods of time when traveling.
I've read a number of places (including the fridge owners manual) that you should never run the Gas on the fridge while at a fueling station. I can certainly see why - nobody wants to go boom before reaching the CG form an accidental ignition of gasoline vapors. 12vdc while on the road avoids the need to remember to kill the LP before refueling and relighting after leaving gas station.
If you don't foresee the need to stop for refueling I guess LP would be a fine traveling option with the exception of loss of flame by winds while traveling. I've heard that can be an issue with some fridges.
I however drive a Jeep Wranger and will be stopping for fuel regularly
I may learn better of my above plan but that's what I've gleaned from these forums.
2011 FR Rockwood Premiere A126 Hard Side
TV=2011 Jeep Wrangler Sahara 2 Dr
Reese 66065 WDH, Curt WDH Shank #17120
Prodigy P2 Brake Controller, Mopar 7-pin Harness
B&M Transmission Cooler (#70268)