Just doing a little cross referencing about the alternator "generator" and it's specification. Rated voltage at 28V. Starts charging at 1180 RPM with a 1:3.268 pulley which means that even at idle (~500 RPM) the alternator pulley is doing somewhere over 1500 RPM which is high enough to start charging according to the specification. Rated at 55 amp output is enough to get juice into the batteries while driving about 1 time per week (25 min each way plus idle "warm up" time.
Honestly since one of the starting batteries seems to have no problem while the other is having issues points to one of the cells has gone bad. At a resting voltage of 10.3V / 5 cells gives very near 2.1V which makes a lot of sense. But to know for sure - individual charging and testing is the way to go!
