So to satisfy my curiosity, and to insure I wasn't boiling my batteries, I opened up the hinged door on the shore power unit, as apparently all the information about it is contained within.
Turns out is a common system, the Magnatec series 6300, model 6345. I was happy to see that it also came with the option code C, which indicates it has the charging unit with the automatic sensor. No indications from the batteries themselves that they were being overcharged, IE; acid bubbling out, and the test switch showing the batteries are in good charged condition.
Well that is a relief!
Thanks for everyone's advice/ideas on this matter.
One question remains. Is there a way to run 110 v into the coach, without going through the shore power system? Seems needless to have the power unit working away, when all I really want is to run a 60 watt light bulb for a little warmth. Other than removing a screen, and cracking the window open to run an extension cord through it, is there another method commonly used?
It appears as suspected, that the chassis battery is not being charged. I decided to run the engine up to operating temps, and noticed it turned over pretty slow. I used the dash button for the coach batteries to assist, and it spun much faster. Looks like I will need to stick my regular charger on it from time to time, to keep it up to snuff over winter. I will look into the other options for this matter in the future.