How the battery shut off works depends on the RV I fear but generally it turns off MOST of the house circuits INCLUDING (But not always) the Generator. Some generators have their own battery (most do not) some use HOUSE, some use Chassis.
Odds are its a dirty connection.. I would clean ALL battery connections starting with the house side, Then hook a volt meter to the red lead on the generator (may even be labeled 12V+ or +12V) and to the chassis (Generator's not the RV's. then try to start it using the outside switch while watching the meter.
If it starts: Fixed, if not, did voltage drop, if so clean CHASSIS battery terminals and try again, IF starts: Fixed, if not, did voltage drop, and POST the reponse.
Home is where I park it!