Mark is right on the money. While I would like to help there are several issues at work here, and one of them nobody but Liberty is going to be able to help and that is the Watchdog.
As to the inverter / shore power issue the best I could do is tell you that there is a problem (or you have no problem). I am extremely reluctant to get involved with coaches of unknown history. I am not suggesting yours is one of them, but if it has ever been modified in the past by other than Liberty (for the house) and Prevost (for the chassis) there is no telling what has been done unless previous owners or technicians have documented the change.
I can explain how it is supposed to work right down to the details relating to how your inverters were installed by Liberty, but if the inverters are not original or installed exactly as the circuits were originally set up, at that point anyone that works on it has to start at the beginning.
Don’t despair just yet however. Either Bill in Chicago or Troy in Florida can walk you through the diagnosis, at least to isolate the problem and the Watchdog can likely be sent in for repairs or replacement.