@Kzneft, a few important questions:
1.
How exactly is your generator going to charge your batteries? I presume you mean that the generator is providing AC power that is then used to run an AC-DC charger, but since that's not in your diagram I can't tell whether or not it's going to interfere with anything... how all of these things are connected will be critical to establish the proper methodology here.
2. As a general note, 5ga wire is not appropriate for a 2000w inverter at 12v; the appropriate gauge will be determined by the exact length (round-trip) of cable run, but typically it will be somewhere between 2AWG and 2/0 (00) AWG. Again, this is dependent on total cable run.
3. You should have a fuse or breaker
at the battery on the line feeding the inverter... before the disconnect switch. Also, for a 2000w inverter at 12v nominal, this will most likely be a ~100A fuse or breaker, not the 50A as shown... but this depends on the cable gauge, as the purpose of the fuse/breaker is to protect your cable, not the inverter.
There are a number of other considerations to be taken into account here, but if we clear up these first few, I think we'll be better-equipped to continue with troubleshooting/advice re the proper way to set up this system.