You need to take a ride with someone in back who can measure the voltage at the house battery while you are driving.
Battery charging voltages from the alternator are much lower these days than they used to be. 13.8V is not uncommon. If there is any loss in the wiring, you just are NOT going to get high enough voltage at your house battery.
Does your camper have a good built in charger ? The simple answer may be to run a low power (300-500W) AC inverter off of the engine battery (use #10 wire with a fuse close to the battery) and feed the camper ! Pay extra for a pure sine wave inverter.