To answer your question, yes, the regulator is external on the old ones.

But 14.4V should be enough to properly charge the battery.

Sounds like something may be draining the battery when the engine is off. With it off disconnect the pos cable from the battt and connect an ammeter/DMM inline to measure the current draw when everything is OFF. If it's more than 50 mA or so something is wrong. Start pulling fuses to help narrow down the circuit that is drawing too much current.

I had similar symptoms once in my Maxima.I found there was around a 1 amp drain when everything was off. Turned out that one of the diodes in the alternator was bad.