You never answered if you have electric cooling fans.
Did the car ever run "correctly" if so what had been changed since then?
Like Mattox said, without knowing what the current is doing you don't know what is really going on. At idle you might me pulling from the battery because the alternator is not keeping up.
Post a photo of your alternator rear side view.
Did it do this before the alternator replacement? Reason I ask, many times the reman alternators have a larger diameter pulley and turn too slowly at idle.
