Welcome to the forum.
Well sitting stationary means the smaller critters can climb aboard and chew wires if they have a mind to do so and the opportunity. I don’t know if your furnace and fridge are in the same side/area of the coach, but if yes maybe you have some closely run wires chewed up....or some near the 12v fuse panel.
You say you don’t think the fridge and furnace are getting 12vdc. Best way to be sure is use a voltmeter and check the outside access of each appliance (refer to manuals/schematics you should have).
The other much simpler way perhaps:
Fridge: Any lights on the fridge control panel at all (if equipped)......and is it set to auto mode so when connected to shore power it “should” run automatically on 120vac. Still needs 12vdc for controls as you said.
Furnace: when you set the thermostat to call for heat does the blower start at least? Hear any mini relay clicks inside the thermostat when there is a call for heat?
Are these appliances the only ones not working.....what about 12vdc lights, fans etc?
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