OK, sounds like time to move deeper!
One thing to keep in mind is that the thermostat is simply a switch which is controlled by temperature and sometime they get problems that make them do odd things.
So one way to "reset" their little brain is to cut the power to them, wait a few minutes and then reconnect them.
I find mention that they are sommetimes not getting the right info when we interupt power and need to be reset. But I also am not finding the really good info I was hoping to find, so we may have to stumble along best we can.
Do you happen to know where there is a 12 VOLT DC fuse or breaker to control the heating and air? Since both the heater and air will often use 110AC for the big things like running the blower, if we can find a 12VDC source and cut it off, that is one way to disconnect the power to the thermostat.
If you know where to find the fuse or breaker, that would seem to be one way to kill it for a short time and then reconnect it.
What problems would it be to unplug the RV and also trip some main 12VDC breaker to be sure ALL power was cut off to the thermostat as an easier way to try to reset it?
Another way that I am sure would work is harder to do as it requires getting the cover off the thermostat and taking it off the wall to disconnect one of the wires instead of killing power at the source.
This is a bit of info on what you might find getting to the wires that are often tucked back into hollow wall where you might not find them.
Sometimes figuring how to get the cover snapped off is part of the problem.
Disconnecting the RED wire that is on the thermostat should cut the positive battery supply. In this case it looks like the red meets another red so no confusion but sometimes the red from the thermostat may meet a different color in the wall, so we need to get the right one!
This is what SHOULD be controlling things but there is an old saying in electronics!
We know what they do when they work right but when they don't they can do anything they feel like!!
Fingers crossed that at least you can stop the power use until getting better info?