Another issue with putting on a reman or even new alternator, it that the battery should be fully charged prior to restarting the vehicle. recharging the battery fully via a grid powered charger cannot be stressed enough, especially with the quality of today's remans.
A depleted battery will ask the alternator to prodcee maximum current, and a freshly reman'd alternator cannot handle this before it is broken in properly(if ever).
I had this issue with a reman alternator hundred of miles into its life when I asked it to recharge 3 large very depleted batteries. It almost stranded me deep in Baja, but fully recharging all three batteries, and driving another 50 miles, and all of a sudden it was charging again.
I figured the unbroken in brushes glazed over or popped off the commutator and got stuck in their holders when asked to produce 90+ amps when not broken in.
Most remans have a little CYA note saying to fully charge the battery first, and it is commonly ignored at the peril of the installer.
It is also entirely possible that your previous alternator was fine and the problem lies and remains elsewhere.