First off for the many new coach owners here:  re. alternator, it was not meant to hit the road after dry camping and recharge house batteries.  That’s a major cause of alternator failures.  Recharge with your genset prior to starting the engine.  The load of 4 to 6 discharged deepcycles is much more than our standard alternator can deal with, and is it’s sure-fire demise.
That out of the way, and assuming your alternator hasn’t been abused in that manner or you’ve not dry camped, Gary, check your Magnum panel over the door, aka. “the remote”, and make sure it’s set for AGM batteries and not wet cells or gels.  Some owners change battery types and don’t realize the inverter needs to be programmed for that, otherwise for example the inverter’s charger may try an equalizing charge phase that’s meant for wet cells but may not be helpful on others.  Ditto for the dip switches on your solar controller.  The inverter should have little to do while you’re on the road and is unlikely the problem here.
After ascertaining all that, your ‘06 coach’s BIRD controller may have a bad connection, pinched wire, or other failure.  It’s the Intellitec Bidirectional Isolator Relay Delay on the door in the cabinet over your batteries.  The controller operates the Big Boy, the large solenoid in the middle front of the cabinet.  If the alternator is good, the controller on the highway makes sure the chassis bats get up to 13.3 volts, and then switches charging to the house set.  If your alternator is bad your two chassis (starting) batteries won’t be up to snuff either, and it may only be a matter of time before they let you down at a fuel stop or somewhere inconvenient.  You should use a voltmeter to check the voltage at first the chassis set with engine running, and after a bit the house set.
At a campsite plugged in or when on the generator, the BIRD charges the house set up first to 13.3 volts and then does the chassis pair, just the reverse of when the engine is running.  Also possible is a bad Big Boy solenoid, as some threads here have recently discussed.  It may not be switching over to charge the house set when told to.
Joel