This reminds me of being at sea around the scuttlebutt and listening to the sea lawyers preach and wave their arms. There are far too many ways to connect things especially in a pusher diesel to make all-encompassing statements about how "this-is-connected-to-that".
OP you need help. Standing right by your side as you do this stuff. Even with 50 years of experience I need to stand back and take a good look before plunging into diagnostics on a pusher. It would help you and anyone working on your rig if you had a wiring diagram from the manufacturer. Not the coach part, the chassis part. Secondly you need to know and understand how to tell the difference between an engine starting battery and a house battery. They have different labels and terminals.
Some stuff is hazardous to so and you need to be damned careful doing it. Like measuring the alternator voltage at the alternator with the engine running. Nasty stuff like spinning fans, pulleys, and belts can endanger you and your meter.
You need to make a list. Without a list you are sunk...
How many volts does the single battery have at rest?
How many volts do the twin batteries have at rest?
How many volts does the single battery have when the engine is started and has been running for ten minutes?
"......................"twin batteries".....................................
............................?
On both sets of batteries, is the voltage on your meter climbing, or is it stagnant? This is important.
Note the SHAPE of the terminal posts on the two batteries and the shape of the terminal posts on the single battery. THIS IS IMPORTANT. WRITE IT DOWN.
Stop the engine
Plug in the coach to shore power.
Do the same voltage check on both sets of batteries with the converter running on shore power. What do you see on the single battery. The twin batteries. Is the voltage rising now or is it steady? How much voltage on both sets of batteries?
A voltmeter digital multimeter, WITH THE TEST LEADS PLUGGED INTO THE CORRECT HOLES ON THE METER, and meter set to VOLTS DC, is fine to connect to a battery. The red lead to the positive side the black lead to the negative side.
Auto parts personnel make six dollars an hour and are one step up from a hamburger flipper as far as expertise is concerned. Forget what he said and do what I said. Just don't screw up and plug the red test lead into AMPS. This is a NO NO. Red lead to VOLTS black lead to NEGATIVE. Look for the DECIMAL POINT on the digital display. This is crucial. Take your time.
To repeat, without writing this stuff down on a list you might as well forget checking anything. Troubleshooting is an inverse pyramid of problem solving diagnosis and is a process of elimination. A regimented process of elimination.
Armed with a clearly readable list of facts and figures return to the forum and report what you have found. This will hurdle round one and really start narrowing the problem down.