Battery's won't charge while plugged in

Not enough information. What type RV, Vanguard made class C and trailer/5'er? What wires did you measure across? 12V going in and out of what? 1V where?

If you have power to the interior 12V devices when powered by shore cord but no 12 V power from battery alone, the most likely suspect is a circuit breaker or fuse in the batty cable between distribution panel and battery.

Do you have a disconnect switch? If so the solenoid connected to that circuit is either stuck or not functioning.

If the solenoid is "off" the batteries would get no charge from the converter when plugged in. Note that most newer RV's are set up to allow converter to power the 12 volt circuits, but not charge the battery(s) since disconnected from the circuit.

That would normally mean zero volts read on the circuit to show disconnect and NO CHARGING. If you are seeing only 1 volt of charging with battery(s) connected to the circuit I would strongly suspect a loose ground wire either at battery, converter, or at the frame of RV somewhere on the 12 volt circuit.

Trying to read between the lines here a bit..........

It would appear that ALL of your coach 12 V system is connected together when on shore power.....EXCEPT THE BATTERIES.

Does the 12 V equipment work with no engine or gen running and NOT plugged in to shore power ?? If not, then the batteries are not connected when the engine is OFF; probably a battery relay or solenoid......or broken wire.

Where exactly are you measuring that 1 V ??

You have an open circuit between the battery and the converter panel.

Keep poking around with your meter and eventually you will find some place where you have 12 volt on one side and 1 volt on the other. Repair, replace, clean, tighten, adjust that item. Most likely at a fuse or switch point. Very rare to be mid wire.

Have you had ANY work done lately?

I'm confused too. But lets get some accurate information.

Meter on battery posts voltage?
Meter on battery posts with vehicle running?
Meter on battery posts with vehicle off, but plugged in to power?
Meter on positive and negative terminals at output of converter when plugged in to power?

I'm wondering what the problem could be. Im assuming there is a current regulator and it's the only thing I can see that doesn't seem to be working as get 12 volts going in but only 1 going out. Or could there be something else somewhere I can't see?

i'm confused ?
your plugged in
you can turn on lights etc.. and the batteries DO NOT go dead ?

they must be getting power, unless disconnected, the converter must be working
or the batteries would run down, or the lights would not work if the batteries are disconnected

the converter takes 120v and makes 13+ volts to charge the batteries and power the RV

12v in and 1 volt out ? sounds like you are trying to measure {the INVERTER) that is turned OFF
NOT the converter
the inverter takes battery power and makes 120v to run the TV etc.. when you are dry camped someplace with NO shore power to plug into

Dozens and dozens of links here about troubleshooting...do a search.