Good new on the battery front.
Went back to the RV this Sunday with my tools including a multi-meter, temperature was -18celcius.
House battery both show a 12.52 volts (does say they are fully charge only that there is current).
Started the generator, house batteries still show 12.52 but when measuring on the other side of the electronic house switch I have 13.7 volts. This says to me that the house switch is not letting the current flow.
I saw 2 small fuses and I replaced both with spares ones that I had and "eureka!" house batteries show 13.7V
Conclusion defective fuses on house switch. I have decided to replace the whole switch because it has been there under the hood for 16 years, and thanks to internet the search for the part was very rapid. It's an Intellitec 01-00055-00.