Does this coach have a 30-amp shore tie cable, or a 50-amp?
What does this coach have as a Generator, and is it working? I recently saw a Class A that was 30A shore tie service with a 5500-Watt generator. The second A/C would run only off of the generator.
The Coleman Mach A/C will have at least two Capacitors. One for Fan Run, the second for Compressor Run. Each has to be good for that part to run. Chances are, there is also a Start Capacitor and Start Relay for the Compressor. You could try substituting the capacitors from the running A/C into the other one and see if the situation changes.
Capacitor failures are relatively common, fortunately more common than compressor failures, or even refrigerant leaks.