Your RV will consume 35 AH daily just to run the CO meter, propane detector and refrigerator. The load is 0.8 amps per hour 24/7 and goes up to about 1.2 amps for the hours that the refrigerator is running.
Your furnace is an additional 6 amps each hour it runs.
The old lights add 1 amp per hour they run, but new LED's are only about 0.2 amps per hour. I have changed many of my light to LED now.
So I would not be surprised if your battery went dead after two days without recharging it. Best thing to do is run the generator about 2 hours during the day, and run the furnace while it is on when you need to warm up. Another 2 hours near bedtime (wary that other nearby campers want to have it quiet at night) and run the furnace while this is on to make it toasty warm inside, so that power is drawn while the generator is on.
Or change to solar power. A pair of 140 watt solar panels will each put out about 50 AH daily, and keep you above 50% state of charge daily.
SunElec.com has a 12 volt with aluminum frame for $229 each. Add to this a 20 amp controller, some UV resistant grey wire from Home Depot, and some mounting brackets (2" aluminum angle 6" long with 5/16" hole for a 1/4" bolt into the panel and 3 - 3/16" holes for #10 screws into the roof) and you have a great system for less than $750.
The way I figure it my $3,000 solar system and inverter saved me $10 a night camping well over 300 times in the first 8 years, paying for itself. Saving that much 3 times since that time - while I was full timing much of 2005 - 2013.
Good luck,
Fred.
