The normal DC OUTPUT coming from your converter when plugged into shore power or generator should read 13.6VDC. If you have a smart mode converter/charger which i doubt then the DC output voltage from the converter/charger can read a slightly higher DC voltage like 14.4 when in boost mode.
I suggest you use your same DC VOLTMETER and measure your car battery and see if it is working ok.
22VDC would blow every 12v item you have connected.
Your basic power setup is 120VAC for alot of your appliances including the converter/charger unit and then 12VDC for all of your DC requirements...
This is basic pictorial showing a typical 30AMP RV Trailer power distribution setup.

You can see from this that alot of items run on 12VDC either from the converter or from your 12VDC battery when you are not on shore power or generator.
You might list the model number of your converter/charger unit.
Hope this helps some
Roy Ken