What charges the house batteries

The rate of charge can vary widely. Don't expect much in the way of amperage from a tow vehicle's 12 volt wires. They are mainly to keep the battery from discharging and little else. Some motorhomes have a decent alternator setup which can easily charge the batteries, others may barely throw in a charge after eight hours on the road.

Depends on what kind and make of RV you have. some pop up trailers do not charge batteries from the tow vehicle but MOST do or at least CAN be charged by either engine in a motor home or tow vehicle in a towed RV.

In most cases they are being charged by the engine alternator.