The car dieing would make sense if the alternator was not working. BTW, don't ever remove either battery terminal connection with the engine running and alternator working; the alternator voltage will spike up and often kill the alternator.
Did you check the 2 wires on the back of the alternator with the engine running? If so, then there should be some difference in voltage between the 2 terminals, if the voltages are the same, then the VR is not pulling current through the field like it should.
The VR case normally grounds to the bodywork through the bolts; star washers under the bolt heads will help. You can add a ground lead if you like but the case must be grounded for the VR to work. That could explain the 'no voltage difference' on the 2 smaller alternator terminals.
