Check Voltage while plugged in to "shore power" at both the output of the converter and the battery terminals.
You should see something above 13.2 V in any case while plugged in in BOTH places.
If you see something over 14.0V it means your batteries are more than 20% down from full and all is working properly.
I would leave the charger plugged in overnight...then unplug and REMOVE the negative battery cable and wait 24 hours before taking a reading with the voltmeter.
It should read 12.6 or 12.7V if the batts in good shape...and in no case less than 12.4 which indicates a severe loss of capacity.
BTW...if you buy an AC/DC clamp meter for about 50 bucks...you can not only measure voltage but you can also check how many amps are going in or out of your batts or how many amps anything in the coach is using while turned on. Handy. Here: