The one problem you have left is that your MH may not be set up to charge the chassis-battery when plugged in for converter/charger to charge the house-batteries. My Fleetwood Jamboree does but not true for all manufacturers.
That could explain the dead chassis-battery. Also; the inverter you have installed is used only for converting 12v dc off your house-batteries to 120v AC for television, or dedicated 120v ac outlets. It has nothing to do with your problem except if the dummies connected it to your chassis-battery.
The inverter should be left off unless powered to run an AC outlet. They can use upwards of an amp per hour, depending on size, if they are powered (not including additional for electronics plugged in.
