Driving w/ Fridge running

[wecker1]

Ok, so I think I remember someone saying that there’s no such thing as a dumb question on the MOC…well here it goes…

Our main trip each year is from our sticks and brick in GA to the family farm in upstate N.Y., about 14 hours. Because of the remoteness of the farm, we like to stock the fridge/freezer prior to departing. As such, we run the fridge at intervals during travel and especially during the last few hours of travel because we boondock overnight and turn the fridge off/disconnect the batteries.
While driving I run the fridge with both disconnects (battery compartment and convenience center) switches engaged and converter on. Fridge stays cold and no problems in that respect. The problem is that this appears to have a major draw on my batteries. I’m assuming here because my batteries show low voltage upon our overnight stop

Three years ago, I reconfigured the Montana OEM battery install from two 12 volt to two Trojan 6-volt AGM. I’m now replacing one of the batteries as it will take a charge but not hold it.

Question: Is my approach in running the system in this manor while driving flawed or did I just get a bum battery?

Much thanks!