The colors you have used in your diagram are misleading and that is causing confusion in the replies.
For AC circuits; black is hot (load), white is neutral, and green is ground. If neutral is bonded to ground while on shore power then current will flow along the ground wire back to the host. This can cause a hot skin condition which is a lethal electrocution hazard!
Read More Here:
http://noshockzone.org/rv-electrical-safety-part-iv-%E2%80%93-hot-skin/
Additionally, UL458 for mobile inverters actually allows for 60V on the neutral. This is not like a structure where neutral is bonded to ground at the main panel. The output from these should never be extended to additional outlets due to risk of exposure to the energized neutral.
Inverter chargers with internal transfer relays should make (connect) the bond while inverting and break it while on shore power.