on my 31e the Chassis does not get charged unless the V10 is running. my truth table is as follows.
Generator power = shore power
shore power = house charging. chassis no.
driving( AKA V10 running) = house charging. chassis charging.
im not sure if this is because i have a cheap thor isolator but i plan to get something like this to make sure when the house is being charged the chassis is too: (or i might replace the isolator with one that is more than a ignition controlled relay and allows bi-directional charging.
Battery Chargers | Auxiliary Battery Charger | Xantrex