OK, after some forensic reading here's my $0.03
There are two scenarios here. Either there is an issue with the 12 volt side/converter sucking a major load and tripping the AC, or you are just plain overloading the system. BTW, I think right now your batteries are dead, so first:
Disconnect the battery (ies). Measure the voltage. If dead/low put a decent charger on and top off. This is to alleviate a massive drain on the converter when you turn it on. Confirm that the batteries are taking a charge. Confirm that they hold their charge when the charger comes off. (After an hour they should read better than 12.3 -12.4V )
reconnecting the batteries turn off all AC breakers, connect shore power then turn on the main. After making sure the disconnected battery terminals are not touching each other or ground turn on the converter. If nothing trips, the converter is probably healthy so turn it back off and reinstall the batteries, make sure they are correctly installed.....and don't trust the last guy that did it either. You can verify neutral being neutral by checking it against the chassis. While you're at it, check that the hot one is not shorted with the neutral. Some continuity will be there from 12V items that you can't turn off. Turn off everything 12V you can think off and then just look to see if there's a blatant short.
Turn the converter back on. If nothing trips you're good. If it does, it (the converter) may well be bad.
Also, how big is the converter....... If the batteries are empty, a sudden 120 amp load at 12V may well trip a 2000W genny, or a 15A house circuit.
Finally, make sure nothing else AC is on when you're doing all this. A water heater is 1400W and all that will run on a 15A circuit, be it house or genny.
I have installed one of these:
They are easy to install and really help managing your load....