My total guess on the red switch is it powers an inverter.
Your dads trailer has a standard converter/charger that runs when he is on shore power. There is also an inverter somewhere in the trailer and it is powered by the red switch. The 120v side if the inverter is also wired backwards so the polarity changes when you turn on the switch. A simple test would be to turn off the switch and unplug shore power. Check the outlets. Now with the shore power still disconnected turn the switch on and see if you get 120V at the outlets.
The battery drain is pretty common but usually takes about a week or two to drain. The smoke detector, the refrigerator board, the water heater, all draw 12v power when they are on. It's also possible that if your father does have a separate inverter it is powering the converter charger. Basically it might be trying to use the battery power to charge the battery.
