First you want to check the camper battery and verify that it is reaching a 100% charge level by having it load tested at an auto shop or parts store. If the battery is OK then the problem lies elsewhere with something drawing more than it should.
With our Lance 845 we have never drawn the batteries down below a 12% discharge while camping and that includes a 4 day period where the air temp never got above 28 degrees. In cold weather our fridge draws less and the furnace runs more but the furnace motor is very efficient. The electronics draw from the fridge is going to cause a problem as it is not drawing that much current either, in the neighborhood of 1.2 amps when propane is used.
The only way to get an accurate sense of what is going on is to install a Trimetric digital charge and current meter in the camper. My Lance panel would show a 100% charge state for the battery when it was really at 78% per the digital meter. With a Trimetric you can see how much current is going into the battery from the truck's alternator or the charger when on shore power and how much is going out with the furnace off and the lights and everything but the fridge is off.
Two batteries are better than one in doubling your camper's capacity and it is one of the least expensive modifications you can do. Both should be the same type, flooded lead acid or AGM.
With my camper the dealer had put in a group 27 battery when there was space for a group 31 battery. It was also a marine battery and not a true deep cycle battery much less a heavy duty deep cycle battery. No reason to pay the much higher price for an AGM unless it is going to be on its side or in a compartment that cannot be vented.
If you plan on doing a lot of winter camping off the grid I would recommend adding a solar panel. A single 160 Watt panel can provide 6-8 amps of charging to your battery and it is automatic. Unlike a generator it runs itself and never needs to be refueled or repaired and it sits up on the roof so it does not take up valuable storage space.