No need to take the alternator back unless you want to; it is common for the parts remanufacturers to just put a ground tab at the outside of this 2nd field terminal anyway for thre older charging system configuration. With the older style VR, it is 100% correct to ground the 2nd field connection. That is the way the older alternators were configured; the 2nd end of the field winding was grounded at the inside of the alternator case. It does not matter which end of the field winding is grounded.
I would ground the 2nd field connection to the alternator case. Not being grounded with the older regulator is almost certainly the reason that the car is not charging.
Once you get this connection grounded, use your voltmeter to check the charging voltage on the battery. It should read 13.7 to 14.3 volts at fast idle and warmed up across the battery + and - terminals. Any significant deviation from this indicates another problem.
if you do not get that battery charging voltage, then put your voltmeter on the green wire at the ungrounded filed connection. if should read a few volts under nomral conditions. If the system is not charging OK, then report your voltage reading at this connection.
