Do you have a multimeter? I wouldn't think the problem is between your alternator and the inverter for the problem you mentioned. (charging while driving)
The inverter converts 12VDC to 120VAC.
Measure the voltage at the starting battery without the engine running. Then measure with the engine running. This should be 13.5 or so. See if this is getting to the coach battery. You may have a Solenoid/switch between the alternator and the coach battery.