Assuming you have a residential fridge...
Maybe install a DC-DC charger for traveling.
It would provide plenty of power to the batteries and you can leave the inverter running to run the fridge.
When running on batteries, While the INVERTER is ON
I would turn OFF the CONVERTER circuit breaker to prevent a loop that would run down your batteries.
Turn the converter back on when you are back on shore power and turn the inverter off.
https://www.montanaowners.com/forums...hlight=charger