I skimmed the answers didn't see this:
Be sure the fridge is on gas. Try the AC with the power converter turned off. This unit can draw a lot of wattage depending on battery charge. If by chance there is electric hot water heater, turn that off. Note the startup sequence of the AC unit. Does the fan and compressor start at the same time? If so try to find a way to get them to start separately. Such as turn on fan, get it spinning, and then hit the cool setting. If there's any "eco" settings on the generator turn that off.
