RE: Inverter tied to existing 110v AC outlets
I will repeat what others have said: Don't do it!!  I know of no fail safe
arrangement you can put together.
And let me point this out.  The factory installed 110v AC outlets are in an
extremely awkward location.  Anything you plug in there means electric cords
running through the middle of the living area.  Putting the inverter in the
cabinet wall behind the drivers seat allows any connected items to have a
cord routed so it doesn't run across the floor.  I have a power strip
mounted to the top edge of that part of the cabinet, above my inverter.
When using shore power then all cords can be kept out off the floor.  And
putting the power strip in that location is a no brainer.  Double back tape
to hold it there and run the cord through the clearance at the back of the
cabinet and plug into the unused 110v outlet in the back inside of the
cabinet, where the refigerator 110 is plugged in.