It seems to me that since everything works on shore power, there is nothing wrong with your power distribution panel. The distribution panel is used whether the converter or the battery is supplying the 12v power. It sounds to me that you have a bad connection in your battery wiring or the wire between the battery and the converter.
Your battery disconnect switch is probably located beside the door, that's where it is in my Four Winds. It is a momentary on switch. Press the top to connect the battery, press the bottom to disconnect the battery.
Don't get confused with the chassis electrical system. The chassis and coach are separate systems except the alternator charges the coach battery when the engine is running.
Class C, 2004/5 Four Winds Dutchman Express 28A, Chevy chassis
2010 Subaru Impreza Sedan
Camped in 45 states, 7 Provinces and 1 Territory