I've never come upon a propane RV stove that needed electricity (either 12V or 120V) to function. The furnace does need 12V power, as do the lights and usually the built-in propane and CO detectors.
More efficient than using the little inverter to charge phones, etc. would be to get a 12V phone charger. It may require installing a lighter socket or two in convenient places. Whether the efficiency difference matters any in practice to your brother in law is another matter entirely.
If his hunting camp is out in the woods, solar may not be the most practical solution to power.
