You don't need the keep it as warm as is comfortable to you to keep the water in the pipes from freezing. Set the thermostat to about 50 F.
If it's just going below freezing the furnace won't be running all the time so even one battery may run through the night.
Can you run an extension cord to your trailer? If you have no appliances on, you would be okay with a 15 amp extension cord to power the convertor to keep the batteries charged.
Or, if you only have one battery, do you have something else with a 12 volt battery, like a riding lawn mower? You could run jumper cables from it to supplement the coach battery. It may be low in the morning and need to be jumped to start, but you'd get your trailer through the night.
2011 Sunseeker 3100
1997 Pathfinder Toad