qdude79 - I have two DROP CORD locations in my OFF-ROAD POPUP trailer with one near the Home Entertainment area and the second position back by a table top where we sleep. This is always on whether we are on shore power or just running off the batteries. I just plug the 120VAC units into these two drop cords that have multiple 120VAC receptacles type drop cords.
I actually run most of my Home Entertainment off the Power Inverter all the time - even when we are on Shore Power or Generator. Never see any disruption...
You can see these two locations in this floorplan drawing..
Roy's image
There really was not enough needs to have my few wired 120VAC receptacles on the Power Inverter. If I had a larger trailer then I probably would want to do what you are asking about...
As you can see in the drawing I also have second POWER INVERTER running 1500WATTS Pure Sine wave but it is too much power drain for my present battery setup. It also had a problem where it would trip my Ground fault detection GFCI breakers. It is installed but not used. I would just hookup a short jumper between the Shore power cable and the 1500WAtt 120VAc output connector on the side of the trailer as indicated in the drawing. A later project when I get a bigger battery bank to handle it...
Roy Ken