Two things, the drop in chassis battery from 12.8 to 12.3 is OK if it is due to the very high amp draw of the intake manifold heater. But, were you to release the key (i.e. no more load) it should return fairly quickly to the 12.6+ reading. If not, fully charge and have the chassis batteries load tested.
The 12.8 reading at the house battery with engine at high idle (where the alternator should be charging both battery banks) is a problem.
Do you have a diode-based battery isolator or solenoid-based battery isolator. The isolator is the first suspect area when one bank shows charge and the other does not.