Without more info, and as others are suggesting, you need to approach this methodically to determine what's going on.
You blame the batteries. I suggest connecting to shore power for at least 24 hours to ensure they are fully charged, and then take them for a load test. If the batteries are good or bad, the load test will tell. And if one out of two is failing, the pair is just a giant 12 volt battery, so the one bad one means a total fail.
P.S. on this, perhaps your charging system is the culprit, or perhaps your battery connections are corroded and need cleaning. If in doubt about the rig's converter/charger, get an external charger and use it to charge the battery bank.
What kind of fridge? 2018 is kind of on the cusp of the switch from Propane/120 volt absorption fridges to the "new fangled" 12 volt compressor fridges. 12 volt compressor fridges will eat about 35 amp hours (AH) per day all by themselves. An absorption fridge's 12 volt demands on propane are nominal. Not insignificant, but negligible when one starts with 110 USABLE AH in the battery bank.
The
furnace will draw about 10 amps MAX when running...for the blower mostly. It's cold so one must estimate the duty cycle. Below freezing, the furnace might run on a 60% duty cycle...on 60% of the time. Overnight, that means for 8 hours the furnace will be running almost 5 hours, at 10 amps/hour = 50 AH. But based on the link, even that's a high estimate. Between the fridge and the furnace, getting through the night should be a piece of cake. BUT YOU WILL NEED TO RECHARGE DAILY IN COLD WEATHER. One presumes your motorhome has an onboard generator to top off the battery bank.
Is your furnace on the fritz? Does it run sometimes and not others? One possibility is that the sail switch is getting cluttered up with dust, etc and needs cleaning or replacement. That's a routine maintenance item on a 6 year old rig. There are plenty of other things that might be wrong with the furnace, but that's the most likely culprit.
And what about other 12 volt loads? You mention the furnace, but you make no mention of lights, water pump, slide(s), leveling jacks. Have you tested the battery condition by trying these other loads? If they all work but the furnace doesn't, then it may not be the batteries.
None of us can tell if it's the batteries, the charging system, or the furnace based on your initial post.
Good luck.
