One quick comment, be careful of the inverter"neutral" many times the inverter doesn't really have a true neutral. Instead, the so called "neutral" has 60 volts on it when referenced to ground. The "hot" has 60 volts on it. Thus 60+60=120. If you don't use a transfer switch that also swaps the neutral, you may get 60 volts on the neutral of the shore plug. Read the inverter directions carefully. If they warn you NOT to ground the neutral, its going to have voltage on the neutral. I found out the hard way, it was a healthy shock!
I recommend that you use a transfer switch, make it a manual two pole switch, or an automatic switch that switches the hot and neutral.
BTW, I simply put a shore outlet in the compartment that houses the shore cable. When I leave for a trip, I just remove the plug from the house outlet, and plug into the camper outlet. No questions about proper isolation. I have a remote for my inverter, thus just hit a button to turn on the 120vac.
2000 Cherokee 29BH with 6V batteries, LED lights & 400 watts of solar power, flipped axles and raised. 2007 Tundra 5.7L DC-LB with lots of mods. C-co, 8/158th AVN Maint.