I wired my entire camper with 14/2 for 15a/120v, just like a house. At the beginning of the 120v line is a heavy duty male plug. I plug that into the inverter's gfi receptacle when drawing off batteries. (There is no hardwire output).
I also have a short 12/2 cord, from outside to inside, for hooking up to either shore power or generator power. When running off shore or gen power, I simply unplug the 120v plug from the inverter, and plug it into the shore/gen cord's gfi receptacle. Works perfectly fine. No different than plugging in any extension cord.
Not sure if the OP could arrange a similar set-up. Just be sure to use quality parts.