I would go looking for where the current is going. You will need a
DC clampmeter to make this a reasonably easy task.
Check each of the wires going to the trailer and write down the current for each. Follow the largest current flow to see where it is going. The wires will disappear into walls but they have to come out where you can measure again.
The problem with shore power vs truck power can be solved with a voltmeter. Check battery charging voltage separately for truck charging and shore power charging. It looks like there is a problem with the latter but find out for sure.