Bob -
Assuming your TM has the 6332 converter/charger, its total DC current capacity is 32 amps. Some of this amperage (either 7 or 12 amps, apparently a factory option) is available for battery charging, and some runs whatever 12-volt loads you have on (lights, furnace blower, etc). The total cannot exceed 32 amps, so if you were running, say, 27 amps of "appliances", then only five amps would be left over for battery charging.
But you said that you weren't running any loads at the moment. In that case, either your battery was reasonably well charged up at the moment, so it wouldn't accept much charge current. Or there is a slightly loose/corroded connection somewhere in the line between the TM converter and the battery. I would suspect the former - your battery wasn't really flat - in which case the direct connection from the generator wouldn't have charged any faster.
FWIW, my battery never charges any faster than about 12 amps as indicated by my ammeter, even when it is quite low. I am reasonably confident in the ammeter accuracy.
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What if I connected the 12 v cable to the batteries and plugged the TM cord also to use for lights and other appliances at the same time?
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In this case, you have two chargers trying to charge the battery at the same time. I can't see any specific reason why this would be bad, but I'll admit that it makes me nervous. My guess, though, would be that one charger would essentially shut off the other, so you wouldn't gain anything.
Neither of these chargers (or even both of them together) put out anywhere near enough current to damage your batteries.
Bill