You have three independent systems. Two 12 volt systems and 120 volt system. Your plug in inverter is powered by you chassis battery system. It is in dependent of you house battery 12 volt system. The chassis system is charged by you alternator while you are driving. You lights are 12 volt system powered by your House 12 volt system. Your washing machine is 120 volts powered by shore power/Generator. It would not be powered by your batteries. As stated above. We need to know everything that is not working. Does All 120 run off the big inverter? A/C will not. Does that work?