Multiple 2kW inverters connected to same 12V battery bank
When dealing with this high currents you'll also have to worry about the batteries themselves and the interconnections in your bank. If you make a mistake there you will end up in a lot of trouble.

For example if you connected both inverter feeds to the same battery as output then the interconnection to the next battery will be overloaded. If possible put that connection all the way at the other end.



However it's better to upgrade your battery bank voltage to 24V by putting pairs of series batteries all in parallel in your bank. That will drop the current by half for the same amount of power.