We had a 12 volt fridge in our old van conversion that ran a 12 volt battery down in 4 hours, I exchanged it for a simple ice box and bought dry or regular ice for it. Two 6-volt golf cart batteries in series for 12 volts and an inverter might run your fridge for around 8 hours, (the inverter uses power along with the fridge). You could turn off fridge and put dry ice in the freezer compartment to keep stuff cool while driving and hook up to 110vac shore power if available where you stop for the night. This would save your house batteries for lighting, running the furnace, fresh water pump, etc. BTW, running batteries down will shorten their life considerably. A converter/charger will charge the batteries slowly when you are connected to 110vac shore power or connected to a generator. The engine's alternator will charge the house batteries slowly if connected to them with a relay setup.
12volt batteries should be maintained at 13+ volts. Learn about current draws of 12 vdc and 110vac appliances and devices and converter chargers, and use a voltmeter to monitor battery charge levels. Keep electrolyte levels above plates using distilled water.
