When you are plugged into shore power, 120v does a pass-through on the inverter for all the 120v plugged-in stuff. You can see this by turning off the 'salesman switch' when you are on shore power. When it's off, no 12v ceiling lights, fans, pump BUT your 120v TV, microwave, plugs etc will still continue to have power. That's the way it's supposed to work and does so on my Vectra.
You mention a Xantrex inverter... that's a replacement as the original build was a Dimensions unit, which I still have in my Vectra. If it's like mine, you cannot trust the battery display while plugged in or running the gen, as the batteries are (hopefully) receiving a charge and it will always show full. To get an accurate read on your batteries from the panel you need to disconnect from shore, turn off the gen and the engine, and see what the panel says (or use a battery tester.)
I think there's nothing wrong on your 120v side, but the 12v side has an issue. Try toggling the 'saleman switch' off/on... you should hear a relay click and things (overhead lights etc) go off/on. Check your inverter to see if there is a reset switch on it. If the inverter has an issue you will have no 12v in the house nor will the house batteries be charged.