When plugged in or running the generator, the house batteries ARE being charged but it appears the chassis batteries are NOT being charged? If the house batteries ARE being charged by the inverter/charger, then 1> the inverter/charger is likely working properly but 2> the battery combiner (BIRD/Big Boy, ECHO, etc.) may not be passing the charging voltage through to the chassis batteries.
12.55v on a stand-alone 12v battery is nearly fully charged... 12.65v to 12.7v is fully charged. When the inverter/charger is charging the batteries, then you should be seeing the higher charging voltage coming from the inverter/charger (not the batteries' voltage) that is 13.3v or higher. When the batteries become fully charged, then the charging voltage will settle down to 13.4v to 13.7v and maintain that 13v+ level.
On the other hand, if your coach engine is running and the alternator is charging batteries, then you should be seeing a charging voltage of about 14.1v+. Again, you would be seeing the alternator's charging voltage, not the batteries' voltage.
If your answer to my first question above is YES, then I am guessing your battery combiner (BIRD/Big Boy, ECHO, etc.) is the first place to look.