There are many places to have an alternator bench tested if you remove it, or you can drive it to a facility for testing on the rig.
You say the chassis batteries go dead in a few days; is that a few days parked & plugged into shore power ? or a few days of driving ?
Have the batteries ever been load tested ? Bad batteries can lead to all sorts of issues with both the chassis charging circuits and the convertor charger.
Is this a new problem on a coach you've had for a while ? Or a new to you coach?