Bob,
As discussed before, there are current loads coming off the chassis batteries, mostly I believe they are computer/electronics related to the Cat motor. There are others like radio electronics that hold memory settings etc. Without something like a Xantrex echo charger you only have the main engine to charge these batteries when the engine is running. All the time it is not running, it is discharging the batteries at some rate. I know that you have been speculating that the alternator is shorted and drawing down the chassis batteries. If you have a meter that will measure 10 amps DC you could put that meter in series with the sensing leads on the alternator and see what the current draw is in a static mode. You could also lift the chassis battery plus leads and put the meter in series with that and see what the static current draw to the whole coach is. That would tell you if the alternator is doing the bulk of the discharging. Have everything turned off that draws current while you take these measurements (lights, etc).
The main charger only charges the house batteries as others have mentioned. If you have a continuous duty solenoid for the emergency start switch you could put another switch in its place, that is not a momentary type, and use that system to tie the house and chassis batteries all together. That would then tie the chassis batteries to the house charging system. I did this in my last coach and would tie them all together for about 8 hours a week for charging. That worked but you had to remember to couple and decouple these systems on some schedule.
You mentioned that the house batteries were measured to be 9.5V. I indicated that this is a fully discharged state. When you had the engine running they came up to 12V. That indicates that you have charging taking place and that the alternator has raised the battery voltage by 2.5V. Without knowing the current at that voltage you do not know if the alternator is doing its job or not. If it is 12V and 165 amps it is doing its job. I have seen this condition before, that the alternator cannot put out enough current to raise the voltage to 14V given the severe load of the batteries in the discharged state. They will come up in time but battery and charging measurements need to be taken with light to moderate loads on the alternator, with batteries that are not severely discharged, if you are going to go by voltage measurements as your charging systems measure of health.
I'm not convinced the alternator is bad. If you fully charge the batteries using an external charger to 12.6V when the charger is disconnected for a half hour or so, and then run the engine you should measure 13.8V to 14V on the chassis battery. If not, then I would pull the alternator and have it checked. In the end you will need an echocharger or some method of keeping the chassis batteries charged while the coach sits. The loads are just too significant for the chassis batteries to handle, for any significant time duration has been my experience. Hope this helps.
Regards Ed