Two batteries of any size, will not feed an inverter very long if there is any draw at all. You need at least 4 large deep cycle batteries or a generator.
Don't know what your frig draws, but it will use a lot of 12vdc inverted to 110vac.
I have 600 watts of solar, so I need a lot of batteries [5 x 125 amp hr bats] to store juice for a 5,000 watt inverter to feed a microwave, A/C or fridg.
2013 Silverado 2500 HD Duramax/Allison Tuned
Aviator Wright Flyer #1919
"First In, Last Out". 11B4Y
DAV, MOPH, VFW, 5/7 Cav,1/8 Cav Assoc.
11th ABN Pathfinder Co. N7MIP