Jim,
If I understand the scenario and what you wrote this is a genset with an electronic inverter built in. If the air unit was running then the genset and built in inverter must be operational. When you kicked off the main breaker and the genset died when you kicked it back on it may have had too much of a sudden load to come up off idle and died....maybe.
I think you are implying that the main house charger inverter system in the storage bay is not passing the 120V through it, nor is it supplying 13.8V or so to charge the house batteries. There is a 30 amp breaker in the main AC panel that feeds that, you might try flipping that breaker on and off. I am a little fuzzy on what is happening but it sounds like you have a meter and some experience, so take some time and trace where you are losing the AC 120V. It could be at the input to the charger/inverter and like you say that is not working even as a pass through.
Later Ed