Your 12-VDC COACH power system has a fuse panel that is wired with; 1-a 30-Amp input line that powers all of the 12-VDC circuits which goes directly to a 30-Amp fuse and 2- multiple wires from all of your fuses to the individual 12-VDC circuits in your RV including your Air unit and Furnace.
Any ground wiring on your fuse panel would be for some special circuitry on the fuse panel itself, and not for your AC and Furnace which only use 220-VAC for the AC and Propane for the Furnace, functionally.
But, your Temperature control panel does use 12-VDC to manage the AC and Furnace.
So, back to your "HOT" common wire on your COACH fuse panel. If you have a multimeter, you should check the connection on the fuse panel and se if it has any voltage from the connection to a good solid ground. If it does, then it is a hot wire and maybe someone has swapped a fuse ot with one that is a large value and does not blow. Many people will replace a blown fuse with a larger one and forget they did this which can be quite dangerous for the RV owner, and can even cause fires.
Each fuse in an RV is a certain safe value that is designed to blow only if the circuit draws more than the safe amount if current.
And one more thing, your situation can be dangerous and does need to be resolved as soon as you can.