Your description of what's working is correct for a failed solenoid, or solid-state isolator. The batteries are not connected to the 12v circuit.
When plugged into shore-power the converter/charger can power the 12v circuit with batteries out of the loop. The engine alternator can still charge the batteries.
A MH of your circa can have some power fluctuations because it needs the batteries in the loop to smooth things out.
I would cycle the battery-disconnect switch on and off a number of times (they sometimes stick). It can also help if you start the engine first and let idle while you try the "disconnect" switch. Increased voltage of 14.5 to 15.0 volts versus 12.7 volts or less can help free a stuck solenoid.
Mark & Jan "Old age & treachery win over youth & enthusiasm"
2003 Fleetwood Jamboree 29