Welcome to the forum. So your coach batteries are charging OK from shore, but not the chassis battery? Do the coach batteries charge from the alternator when you are running the engine (shore disconnected and gen off)? If not, you “might” have a failed “interconnect relay” (also called emergency start relay).......or its control electronics. This is the relay that ties coach and chassis batteries together under certain charging and emergency start conditions. It could also just be a bad connection, etc somewhere.
This relay is physically located inside the Battery Control Cabinet (BCC). The BCC is located at the front engine compartment, driver side, which should be visible when you open the engine bay doors (a black box). If any serious repair is required inside this BCC no shore; no gen; no engine run and battery ground cables should be removed to be absolutely safe. There are schematics and fairly complete documents describing the operation of the BCC components on line (or search this forum) made by RV Custom Products in California.
Also note the interconnect relay functions on sensed battery voltage levels and operational delay timers. So it may not operate instantly or release instantly. There is also a very good video on You Tube of someone actually opening a BCC and describing it in good detail.