Let me throw this out there,,, A year ago I installed a Kyocera 85 watt panel and controller on my small 22' trailer.
I camp allot at the coast where it is mostly overcast and foggy with some nice days thrown in. We also camp inland with combination of sometimes hook ups sometimes not.
The 85 watt panel has done a great job of keeping my two 6 volt golf cart batteries charged up for use at night.
during the day we only use water pump,and maybe some television if raining.
At night we use the heater a few hours after bed and it only runs for ten minutes at a time the most to take the edge off.
My re fridge runs off propane and the detectors run 24-7 (minimal draw).
We have replaced all interior bulbs with LEDs and even the porch light is LED.
We stay as long as the holding tanks can last (usually 5-6 days).
GC batteries have not been an issue and the panel even on cloudy days will put something back into the system.
Last trip I didn't even bring the generator as we have not needed it to recharge, only thing we use it for is running the microwave and the DW hairdryer (if the bathrooms dont have 110v.
to the OP, if you watch your 12v demand use a 100 watt panel should be sufficient to maintain battery power for your needs (lights and furnace).
Although a second battery will help allot, that 100 watt should be fine!!

Panel is mounted above small window to the rear of trailer, sunny day gave us 5.5 amps/hour back into the system,