The reason for using two Group 31 batteries is a bit embarrassing: I decided 14 years ago during my first intro to trailer ownership to move the batteries inside into vented boxes, one on each side of the trailer. Custom built the boxes, ran the wiring and switching. Seemed to work OK, so I kept it, despite some evidence that two 6-volt units would be better. (Group 31s are easy to find, so that was a factor, and switching from one or the other if necessary is also easy, so out of laziness I kept it).
I have yet to go below 50% charge (in order to protect the batteries), so if we camp under the tree canopy things get iffy on the third day if we use heat during the nights. If we go down the road a spell for another camping spot, the car could theoretically charge the batteries up, but generally the
solar panel is enough. My current tow vehicle has a hefty alternator, but so far I haven't tried to use it to charge.
One factor is the MPPT type
solar controller (Blue Sky) which is able to start charging with minimal
light available while being fed by a
solar panel which puts out more than 20v when going full bore. The MPPT does not waste the excess electricity but converts it to the appropriate voltage and has several charging stages to protect the batteries.
Another factor is that I changed the charge wiring from the car to 6 gauge should I need to use it. Otherwise slight voltage drops to the batteries can inhibit effective charging.
Here on the left coast I found the NovaKool at Boat Electric in Seattle. If you want a frig which uses as little power as possible look for a brand with a Danfoss compressor or the equivalent. We no longer turn on the frig two days ahead of going camping any more, since it cools down in a big hurry.