A converter uses 110v power to make 12v power and feed it to the batteries. Inverter draws 12v from batteries to make 110v power. You say your converter runs on 12v??...don’t see how.....Check your 110v breaker panel for converter breaker and switch it off. No more converter producing 12v power when you are running inverter for 110v power. There is nothing at converter for 12v wires to backfeed. Wire your inverter thru generator feed which will go to 110v breaker panel then you can turn breakers on or off to select what you circuits you want on or off.
