Thank you all for sharing your knowledge and providing suggestions.
Acting upon all your input, I went out to do more thorough measurements and tests. Regardless of whether the house battery is connected or not, 15v+ always presents at the chassis battery. To answer one of the follow-up questions, the MH does not have a solar charging system, and the built-in house converter/charger works properly as its charging voltages are below 14v pretty much all the time whether the AC source is shore power or the generator.
I don’t know how long I have been driving it under this condition – the batteries being "cooked" by the alternator… five to six hundred miles maybe? Not sure how much damages have already been done to them although I haven’t seen any noticeable symptom yet. Come to think of it, that the dash console infotainment center is acting strange lately may have something to do with it.
Packing with the knowledge you all provided and the data collected, I will bring my vehicle to the Chevrolet dealer for them to take a look at the alternator. The vehicle is under warranty and I hope they will get my problem fixed without much hassle as it sounds like what would be entailed is a straight alternator replacement…, or no?
