A bigger pulley on the alternator will slow it down and decrease its charging rate.A smaller pulley will spin it faster and increase its charging rate.
Keep the smaller pulley on the alternator IMO.
I always keep the stock sized pulley on my alternators as that is the speed they were designed to run at. Any more or any less and you may have electrical system issues.
I think you have some kind of wiring issue or the alternator is defective.
I suppose your idle speed is correct?