You need to measure the DC VOLTAGE at the BATTERY TERMINALS with a mulitmeter without the shore power turned on. A fully charged battery will read 12.6-7VDC.
Then turn on shore power and the DC VOLTAGE at the BATTERY TERMINALS should jump up to 13.6VDC-14.4VDC depending which charge mode the converter is in if it is a smart mode converter. Otherwise it should be just putting out 13.6VDC all the time.
Also check your battery terminals to be wired correctly. Look for the word "NEG" or the symbol "-" marked on the battery case and make sure this is the terminal cable that goes to the trailer frame ground.
If the battery terminals are wired wrong they must be changed to the correct position. Then look for an in-fuse close to the battery and see if it has blown. Then also check back at the 12VDC Power Distribution Panel for two fuses labeled REVERSE POLARITY. They will be off to them self. See if they have been been. Replace the blown fuses only after you have insured the battery is wired correctly otherwise you will just immediately blow them again...
If the batteries are connected properly you should be able to turn on your ceiling lights in the trailer without shore power turned on. That will tell you all the connection between the 12VDC Power Distribution Panel and the battery is good.
If the battery drains down over a few days then this is telling you it is not being charged by the converter. That is where checking the DC OUTPUT labeled +BATT is important. This will read 12.6-7VDC if the battery is connected and fully charged and should jump up to 13.6VDC when you turn on the shore power.
Here is 30AMP simplified block diagram that might help with understanding how things are wired up.
If your battery stays working for a few days then drains down I am suspecting the converter is not producing the 13.6VDC to the battery terminals for some reason. Either a bad converter, bad connections, or converter not getting 120VAC when shore power is turned ON, etc.
An inexpensive multimeter ($7-$20 from WALMART-LOWES-AMAZON-Any number of auto parts places) is a very handy tool to have tracing all of this out...
Let us know what you read...
NOTE: I live in the RV TRAILER world and realize that the motorhomes may be slightly different but the concept is still the same.
Roy Ken