You should not try to plug the shore power cord into the inverter.
The inverter should be connected to the batteries, then have dedicated circuits to operate off the inverter.
Not sure what you want to run off the inverter. I have two small inverters in my rig. One operates the rear TV and the other operates the sat dish, sat receiver and front TV. I have a plug strip on the front one to power up printer if needed.
Small inverters are easier to install. Some can use existing DC wiring as in my rear TVs. Front one I ran a new #6 circuit to operate it.
We do not use inverter to operate microwave, that is why we like oven in the rig. Coffee is made on old style percolator on stove top.
