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So here's an update.  Inverter seems to be working, charger seems to be charging.  Inverter does have a pass thru which is why it's showing AC loads going thru it.

So I think my problem is the alternator on the motor is not charging, or not charging enough.  Without the generator running the Volts gauge goes down and down and down.  I put a meter on the alternator (red wire, and ground) while it is running but it's around 13.6 or so.  Is there a way to test this alternator??  What should the voltage be while it's running??

Generally you should be seeing over 14v is best. Have you checked it when its on high idle? Some alternators are slow to excite until they see a bit higher RPM.  
The other option is pull it off and take it down to the auto parts store and have them put it on their test machine to validate that its bad.