Your transfer switch will automatically recognize the generator as the primary source of power...ie: if connected to shore power and you turn on the generator, the transfer switch will automatically switch from shore power to generator power.
In your case, by being connected to shore power, running the generator, and also running the engine (which is supplying power from its alternator), you may have caused the transfer switch to malfunction so that now when only connected to shore power, the switch may be stuck in generator power; hence, no power getting to the converter to charge the batteries.
If you run the generator and the engine for one hour, I hope you are also turning on the AC units to provide a load for the generator. Also, by just idling the engine, you will be causing more harm to it than good. An engine needs to be brought up to full operating temperature and just idling will not do that. Disconnect from shore power and take the mh for a 15 minute drive.
Ron