Bill,
I think this applies to your coach, but if not my bad for making an assumption.
Near where your chassis voltage regulator is mounted there is a Vanner Battery Monitor. The manual for it can be found here: http://www.vanner.com/manuals/EM70D.pdf
You can check the chassis voltage at the terminals with the engine running. You may have to pull the push on terminals back slightly to expose the spade. The manual provides the correct voltage ranges and if the voltages are not within the range specified the monitor will light the warning light on the dash. Some versions of the monitor were not as reliable as they should have been and they gave false signals relating to problems. I am not saying you don’t have a failure in your charging system, just that you can check voltage values conveniently at the monitor to verify voltages. If they check out the monitor is bad, if not at least you know the warning light is correct.
It sounds like your coach has a dedicated 12 volt house alternator, so you are likely to have a chassis alternator that essentially charges the batteries without going through an isolator. If you want to check it out the easiest way is to apply 24 volts directly to the field wire or terminal on the alternator from the batteries. Start the engine and if the alternator is OK the voltage will continue to climb unabated past the normal regulated voltage of about 27.7. Either kill the engine or disconnect the power from the batteries to the field terminal or wire because unregulated voltage can damage coach components. I suggest having your tester hooked up to read voltage so your hands are free to either shut the engine down or pull the wire once you see voltage reach or pass 27 or 28 volts.
What you see if the voltage reaches those level and beyond is that the alternator is functioning. If it is not working the voltage will not exceed battery voltage. Should it not work there is a new alternator in your future. If it does work, it is probable you have a voltage regulator that has malfuncted (a technical term).