6 volt question

First: is your 12/6 charger rated for 14 Ah batteries, or is it a 14A charger? A 14 Ah battery is a quite small battery, such as a motorcycle battery.

Assuming it is for a 14 Ah battery, I would suggest getting or borrowing a more substantial battery charger (simple and dumb is fine here) to charge the golf cart batteries, and then once they're charged you can use whichever little charger is more convenient to maintain them. At 5.9 volts, they're quite substantially discharged (down to about 30%), and it will take a very, very long time to bring them back up to charge with a 2A or so charging current. A 10A charger would probably need somewhat over a day.

For most chargers, you'd probably get better results with them in series as a 12V battery. Most chargers seem to have the same current output in 6V and 12V modes, and so the actual power delivered is half at the lower voltage (or, put another way, the charging current gets split two ways). Doubtless there are some exceptions to this general statement.

Once charged, the battery minder probably would be sufficient to keep them topped up, though realistically letting them sit over the winter in a cool place disconnected would also be fine once they're fully charged. Self-discharge of a fully charged battery in decent condition and cool temperatures is pretty low.

Charge them in series.
You could be overloading the little charger if the batteries are down. If they are fully charged, you should not have a problem.