That much difference in age and condition, I would use them separately, because the battery at 12.6 will give up charge into the weaker one, without it actually storing any more energy.
I have a pair, wired in parallel when installed new, but usually one gets weaker first, and when I detect that happening, I'll split off the bad one and use the good one, until I can replace both.
At least twice a season, I'll disconnect the batteries and separate them, to charge them each with an external charger.
What do you know about the 12V line from your generator? Is it a smart multistage charger? Is it rated for more output than your converter charger? Usually the fastest way to charge from a recreational generator is to use the 120V output to feed a smart charger with peak output amperage rating number that is at least 10% and up to 20%, of the number that is your amp-hour rating on the battery.