Originally Posted by DougW
The vehicle charge system will recharge the RV batteries while you are driving, if the electrical system is properly set up. You should have no problems with overnight stops as long as you are not wasteful with your power usage. If you are doing the trip soon the bigger worry would be if the furnace runs a lot, it can use the batteries up on an overnight stop.
Especially if driving long days. If driving 8-10 hours per day even a puny 5 amp charge rate from the tow vehicle will replace 40-50 amp hours to the batteries.
To the OP:
To get a better idea of what your tow vehicle is ACTUALLY delivering to the batteries, take an actual measurement. Use a clamp type ammeter and with engine running at a fast idle and measure current flow into the batteries at the ground/negative cable.
Do this two times, one with refrigerator shut off, record reading, then again with the the refrigerator running.
A positive current flow will indicate charging and negative, discharge.
Remember, the refrigerator only runs a percentage of the time so when it's not running the TV alternator is replacing some or all of what it used.
If enough charge current isn't enough one alternative is to add a DC-DC charger like the 20 amp Renogy DCC-1212-20. Even with stock wiring it will yield 12-15 amp at the house batteries. $127 is a lot less expensive than a generator, ESPECIALLY if driving long days between stops.
As for using up the batteries overnight with furnace running, a lower thermostat setting, sleeping bags, and flannel 'jammies' or sweats can conserve a lot of propane AND battery. You really just need to keep temps inside high enough to keep things from freezing. (the dog will become very popular too