My 10 cuft residential fridge draws about 120 watts (one amp) @ 120 volts AC when the compressor is running.
On an inverter this will equate to about 11 amps at
12V DC including 10% for inverter overhead.
Two 100 amp hour batteries will give about ten hours of compressor duty at a 50% discharge rate. (The compressor does not always run)
When towing the trailer, my TV alternator will run the fridge while charging my batteries at the same time.
For me, a cheap ($400) apartment fridge was the best answer. I am at over a year in with my big fridge, no problems at all to date.
Brevi tempore!