There are multiple strategies for hooking up and inverter. The small (1000 watt) size of the inverter makes some more practical than others.
The 1000 watt inverter is an alternating current 115 volt power supply. A generator and shore power pedestals are as well. Except in certain situations, only one can be connected at a time. More expensive systems use a transfer switch to connect one at a time and to reconfigure the service entrance to the needs of the different sources. This is probably more complicated and expensive to install than you are willing to do.
Plugging the shore power cord into the inverter is another way. As you noticed, certain appliances need to be excluded when you do this. The charger/converter is one that must be turned off. My Kodiak Cub has a dedicated circuit breaker on the service panel that can be turned off.
Air conditioners, microwaves, residential refrig, electric water heater, and any other appliances that consume large amounts of current need to be off.
The 1000 watt converter does not supply enough power to run what would be one normal 15 amp household circuit. 2000 watts would be needed for that. Look at the specification labels on each appliance you want to run. The total of all devices run at the same time must be LESS THAN 1000 watts. 12 volt lights and other 12 volt appliances are run from the batteries. They do not count in the total AC power to be run from the inverter.