Hi,
I have exactly the same problem with my wife's grand Cherokee, if your alternator and battery are good and all connections are good then it's the voltage regulator in the computer that is bad, this is what is wrong with my wife's jeep, I'm going to fit an external voltage regulator to the body of the car, I'm going to splice the cables from the ones on the rear of the alternator to the voltage regulator which instead of the computer controlling the voltage the alternator kicks out, it will be the external voltage regulator that controls the alternator power output, this is all you need to do to fix your charge problem, I'm going to order a voltage regulator when I get home.