I think there are two different topics at play here.
1. When the grid is down, I want my single 120v output inverter to feed a subpanel that has L1 and L2 inputs.
2. When the grid is up, I want my subpanel's L1 and L2 to be on my main panel's L1 and L2 for reasons to keep my house load better balanced and to make my subpanel easy to connect to my main panel. BUT I also want to have my invert's charger connected to the grid so it can keep my battery topped off.
Are those the two topics that you understand to be goals?
You will have to have some sort of transfer switch or two input subpanel with a lockout toggle between the two inputs. My subpanel has 2, 60a two pole breakers with a mechnical interlock to block the one that is off from turning on.
LV6548 charger spec....."120A Utility Charger (120A at 48V = 5.7kW or 48A at 120V)" Yes you will not normally find a 50amp 120v breaker. Edit....Spoke too soon.
They do exist.