Inverter wire into RV 'house' circuit question

With the grounds you have two choices, and you may find they are both the same.

Step one, With the Inverter NOT POWERED, check to make sure the ground pin on the outlet is actually connected,, Good chance it is not, if this is the case it makes life real easy cause both options are thus the same.

Option: 1: Connect both Mains (Shore/generator) and inverter ground wires together

Option 2: Connect the Mains ground to the load line and forget the line from the generator