The Big Boy-BIRD system acts as a bi-directional system for charging all your batteries. If your coach is on shore power or on generator power, then your inverter should be charging the COACH batteries (the 4 or 6 6v batteries). When the main motorhome engine is running, then its alternator is charging the CHASSIS batteries (the twin 12v batteries). When either set of batteries gets charged to 13.3v, then the Big Boy-BIRD system allows the charging current to cross-over to the other set of batteries. Thus the bi-directional nature of the Big Boy-BIRD system.
As noted in the linked message in my prior post, the inverter needs to be programmed such that it charges the COACH batteries to at least 13.3v in order for the bi-directional cross-over function to kick in to deliver the inverter's charge current to the CHASSIS batteries. Likewise, the main engine's alternator must get the CHASSIS batteries to at least 13.3v in order for the bi-directional cross-over function to kick in to deliver the alternator's charge current to the COACH batteries. If either the inverter or alternator do not supply sufficient charging voltage to get to 13.3v, then the other set of batteries won't receive charging current.
Here it's important to note again that if the COACH batteries are down and the main engine is started, then the alternator will be asked to charge the COACH batteries at a high rate of charge. That high rate of charging is too much work for the alternator and will eventually burn it up. Thus, if the COACH batteries are down from dry-camping, then before starting the main engine you should run the generator for 30 minutes or more to get the COACH batteries up to at least 12.5v or so BEFORE starting the main engine. Before I was aware of this I replaced one alternator to the tune of $400 more or less.