In our Navion, the generator feeds the AC side of the electricals to light up the AC coach receptacles. No inverter required when we run the generator or are plugged into shore power. If I understand it correctly, the inverter draws 12V from the batteries and then turns it into AC and feeds a few of the same receptacles that will run off the generator or shore power. That's probably why the receptacles are hot when you run the generator. If you're not getting AC at those same receptacles when not on shore or generator, the problem is with the inverter and 12V batteries side of things. If our coaches are designed basically the same electrically? Caveat: I'm not an expert nor an electrician.
Mike. Comments are anecdotal or personal opinions, and worth what you paid for them.
2018 (2017 Sprinter Cab Chassis) Navion24V + 2016 Wrangler JKU (sold @ ????)
2016 Sunstar 26HE, V10, 3V, 6 Speed (sold @ 4600 miles)
2002 Roadtrek C190P (sold @ 315,000kms)