Sounds like, instead of "rigging" the system into thinking it has shore power, you need more solar and more batteries and let the setup work they way it was designed.
I'm still getting on my feet in a new state new job still finding a place to park it for good. And until I'm able to have someone help install the solar panel system correctly I'm doing it the cheapest way I can. That's why I asked if you could plug the shore power cord into the inverter as a possible short term solution until I'm fully set up with solar correctly or have a place to plug into an actual better shore power system. I didn't know if it was possible to do or not I'm still figuring the whole solar stuff out all on my own with my daughter. She was trying to figure stuff out and thought hey is that possible to just do it that way obviously not all the time like a normal house or campground power system and not using everything in the camper like normal mostly just the wall outlets for tv mini fridge microwave(when needed) and small ac unit or space heater when needed and the panel system came with 2 lights that light up the whole thing so I wouldn't be using the camper switches for light. Or a water heater because I'm fixing all plumbing still.
Fridges and microwave (especially microwave) have pretty large amp draws. More than one battery can support. You either need more batteries and a way to keep them charged or a different power source. A generator would be a simple option although not cheap. Maybe find a state park that's cheap and has electricity, harvest host, etc. I appreciate the creativity and your position, but I am not sure you can perform what you are asking with what you have.
