As suggested, you must start with a voltmeter across the batteries to see if the converter charge is getting there. It appears you have both of the positive leads connected by a jumper so they should be getting the same charge. Close enough for real world. Your charger is not large and it appears it my be about 40-45 amps according to the specs. If you are running other things such as lights which draw 1.5-2.5 amps each that is subtracted from the available output of the converter. It could take ten hours or more to fully charge based on the design of your your charger. Just look it up and visit the charging curves.
In any case, battery age should be ignored. I have seen brand new batteries fail. With them in parallel one can easily discharge the other if bad.
What most concerns me is that you are saying they appear low immediately after disconnecting shore power. Either they are not getting charged, one or both are bad, or you have loose/corroded cables. Your cables must be shiny clean and tight. With 12 volts it is easy to get a loose connection. If there are wing nuts involved you have a better chance of loose connections too.
Does your camper have a disconnect switch? It may be off and the batteries are not getting charged. Seems I have looked at a schematic months ago and found some interesting setups.