The alternator in my CRD is different than your 3.7. So I dont know exactly how your alternator is supposed to behave. I know my alternator has its own internal regulator and will function just fine without any input from the PCM.
If you have already tried two different alternators and got the same result (assuming both alternators have tested good) then I suspect the problem is in the wiring harness.
So check the wiring out really good. Look for any rub marks on the harness where insulation is worn away creating a short.
Thats all I can suggest.
Very strange problem.
I'm sure that adding a external regulator will help.
https://www.youtube.com/watch?v=BI7oFEcDQzohttps://www.youtube.com/watch?v=utXjxwPAcHk