No, the converter is what converts AC power to 12 volts to run everything and charge the house battery. The battery isolator keeps the 12 volt circuits in the rv from running down the starter battery.
It sound like your converter isn't charging your battery and your isolator isn't isolating the two systems.
Since no one has responded to your schematic request, I think your going to have to trace down the power distribution circuits in your RV and draw your own schematic. You seem to know your way around a DVM.
I've done several, it just takes time, and once done you'll be able to figure these type of issue out quicker.