Kevin,
Are you sure that your coach has two invertors? We have nearly the same coach with factory installed residential fridge and eight house batteries, we have one Magnum Invertor/charger. While there are four circuit breakers in the AC panel labeled invertor, two are output to the invertor/charger (from the transfer switch) and two are input from invertor/charger (to the AC panel).
The Aladdin system can be very useful for preliminary troubleshooting certain electrical issues, I wouldn’t rely on it to condemn any components.
You are always going to have draw on the house batteries, i.e., PCB board #5 in the front run box is always hot, regardless of the house battery disconnect and/or the ‘salesman switch’ position. PCB board #5 powers such things a radio memory, various 12-volt detectors and the like. Also, the Aladdin system itself will be drawing some power.
The difference that you are seeing when cycling the chassis battery disconnect maybe from the BCC/BIRD circuit board (#R6) in the rear run box, this PCB utilizes both chassis and house battery power. Starting the engine is probably triggering the isolator circuit that was killed when you used the battery disconnect(s).
Have you load tested your batteries? I would be suspicious that one of your ‘new’ batteries may have an issue. We had two of our eight batteries with bad a cell, they’d take a charge but wouldn’t hold with the inverter on and fridge running.
Are your chassis batteries also depleted in the morning?