The alternator should be large enough to fully charge both battery banks in a few hours of driving, so more than "some" depending upon battery discharge and driving time.
The 50A RV service is 120/240V 50A 4 wire. This is the same service as a house except houses are generally 100 to 200A. A house supplies both 240V and 120V appliances. And appliances can use both voltages like a oven with 120V control and lights. Very few RVs have 240V appliances because they will not work with a 20 or 30A plug or a 120V gen.
My charger/inverter has a 120V 30A input for the charger and a transfer switch that routes the 120V to 2 output circuits that power part of the coach. When the inverter is off the output power comes from shore power or the gen. When the inverter is on then it's input power comes from the 12V batteries and the transfer switch routes it's 120V output to the same 2 AC output circuits. Your charger and inverter may be different but the operation will be similar.
Very rare for a battery and inverter setup to supply power for high draw appliances like A/Cs, HW etc. A 15A A/C for example would require about a 165A draw from the batteries and that is massive. Hence the common gen for that purpose.
Another transfer switch chooses between the gen or shore power for the RV. Generally it defaults to shore power until the gen is running and then switches to the gen power.
I never run the gen when plugged into shore power and not because the transfer doesn't work but because should if fail for some reason with a short it will definitely let the smoke out as you suggest.
Transfer switches: Automatic Transfer Switch or ATS.
2009 Holiday Rambler 42' Scepter with ISL 400 Cummins
750 Watts Solar Morningstar MPPT 60 Controller
2014 Grand Cherokee Overland
Bob
