A key bit of information that would help offer a practical solution here is how much current the refrigerator draws when operating.
In my truck camper, my 3-way fridge draws around 12 amps when running off DC. When I originally wired the receptacle on the truck bed for the camper connector, I just used the factory +12V lead (#12 wire) in the factory wiring bundle to power the trailer. When driving with the fridge running on DC for 5-6 hours, the current draw would cause enough voltage drop through the factory wiring to eventually draw down the battery to about 60%...meaning that when I got to were I was going, my battery was down to 60% or so. With the smaller wire, the voltage at the battery with the fridge running was below full charge voltage (about 12.7V) so power was flowing both from the truck system AND the batteries until the batteries equalized at the same voltage as the feed coming from the truck, once losses in the cable had their effect.
I solved the problem by installing a #6 wire from the junction block under the hood where the factory wire came from, all the way back to the trailer plug in the bed. Voltage drop through the larger wire was minimal and the voltage at the battery was high enough to keep it at it's full-charge level.
My longer term and more flexible solution is going to be to put a 1000watt inverter under the hood of the truck and run 120VAC to an outlet in the truck bed and to the camper (with disconnect, of course) and then use the installed 30A charger/converter to run the refrigerator and charge the battery in a normal manner. The refrigerator works much more efficiently on 120V than 12V, especially if you haven't pre-cooled it before leaving on a trip. Of course I could always run it off propane, but I'd rather save that for cooking/hot water.
