I would not recommend doing it that way!
Most of those so called 12 volt outlets were not wired or the actual cigar lighter jack is not made to pull more than 10 amps.
On my 30 foot fiver i also had 2 X 6 volt and I put a 2000 watt inverter with remote on and off control, then plugged the 110 shore power into that, THO you need to make damn sure you can turn off or unplug the AC to DC converter!!! Make sure the Fridge is locked into Propane mode. I had my AC circuit breaker panel marked... I was lucky the fridge and AC to DC converter were on the same circuit breaker so I turned them off when connected to the Inverter!
With this setup I could make coffee in the morning without running the Generator
My wife loved this, she hated running the Genny just to make coffee. Especially traveling and stopping in rest areas.
At night hit the Off/On remote kill all 110 power!!