When we run the generator for the A/C while going down the road, I turn off the 'charger' function on ours and just let the alternator keep the batteries charged. That way the inverter isn't working and is ok. We also ran into a problem when we are running in 100+ heat and plug in at the park, the inverter will indicate overheated condition - just turn off the charger function (the batteries are charged up after a few hours on the road) direct a fan to circulate cool air from the a/c into the area with the inverter, and in about an hour, hit charge, the inverter goes through the cycle and returns to float.
Barb