I agree with above use of the inverter.....I have found when driving, the engine supplies the power to keep the house batteries charged. The only time my house batteries loose charge, is when they are powering the fridge but there is no charge power coming to them from the engine, generator, or shore power..
additional comment: when you use the inverter, it is taking power from you 6v or 12v battery system...make sure those batteries a well watered, or they will not hold a charge...if they are hard to get to purchase a battery romote watering system....then you can check them in 60 seconds....true story
when I am driving my motorhome, the fridge runs on engine power, not the batteries.....the only time the fridge is running only on the batteries is when the coach is not plugged in, the gen is not running, and the engine is not running.