Cells in the batteries may not be capable to fully charge, i.e. bad cells. How old is the battery? If the battery is good, and the alternator is new, you might replace the wire harness to the alternator. Last thing would be is to replace the voltage regulator...I don't know if the VR is integrated into another component, just know older technology. VR's has a reverse current relay that connects the alternator to the battery until the battery is fully trickle charged (after starting the car)... When the battery is fully charged the reverse current relay unlatches the alternator to the battery. The problem you may be having is the reverse current relay never latches (closes) after engine start and you may be running from the battery. A simple way is to put a volt meter on the battery and while in park, press the accelerator pedal moderately (~4000-4500rpm). Look for voltage drop on the meter while at the rpm. If voltage drop is significant, then you are draining the battery and the alternator is not powering the circuit. Since you said the alternator is new, again it could be the harness as well. The reverse current relay could also latched closed, which would trickle charge the battery, but stayed latched when the engine is off. The closed latched relay finds a ground with the engine off and drains the battery...so when you restart it in the morning the battery amperage is low. Google reverse current relays as related to voltage regulator and you'll see what I mean. Best of luck.