I don't know how familiar you are with camping trailers , (RV's)

I own a a fifth wheel camper and it seems you could very easily got to a rv dealer and get a snap cover for a an electrical cord use a cord of your choice and you have a way to plug it in to the house without getting zapped It will require you to drill about a 3 inch hole for the snap cover and as far as the inverter if your truck has a 12v hot wire to the plug, use that to run the inverter.

I have a 2000 f350 and mine has one from the factory