[Motor31]

It is not the switch that is the issue it's one of amperage draw. The fridge and water heater are both high amp draw items when on AC voltage. The inverter would be drawing 12 volts from your battery bank to supply that AC and would drain the bank very quickly if the inverter could handle the load at all. The fridge and water heater are designed to run on propane and 12 volts when shore power is not available. The drain on your battery bank at that time is minimal. Trying to supply power to AC items like those would leave you with no power in short order. Your air conditioner is another item that is not connected to the inverter as well for the same reason, batteries cannot provide power for 110 volt high demand items for any real length of time.

That inverter is meant to power low drain items like a high efficiency TV or your lap top and charge your phone(s). You can't get something for nothing.