Mr. 'Dude,
Does your LY have an inverter/charger set-up or a standard converter? It sounds like you have an alternator problem, or possibly a battery isolator problem if you are getting 13+ with the gen or shore power and not when the engine is running.
I'm not really familiar with the Airstream set-up on the LY, but if it is similar to most late model MoHo's, I would start checking voltages at the alternator (source) and work inwards to the batteries.
Contact Workhorse for the location of an authorized service cemter close to you and do let us know how it turned out.
