Check Charging System Indicator

So I drove my explorer down from NY to GA, and
on the way down the AC gave out. Since it’s hot
and the AC wasn’t working, the Explorer has been
sitting in the driveway for the past month. The other
week I went to start it and it struggled to start. It
made a squealing sound and then a pop, and I
noticed smoke coming from the engine. I checked it
out to see the serpentine belt shredded. I began
feeling around for the culprit, and realized the
alternator bearing was completely seized.

So I replaced the alternator and threw in a new belt,
thinking everything is good now. After about a day
of driving, I started getting a “check charging
system” notification on the dashboard and a little
red battery icon. It would appear, then disappear,
and then appear again at what seemed to be
random intervals. I drove to Advanced Auto Parts
and they tested the battery and alternator. They
confirmed the alternator was not putting out
anything. So I wiggled some wires and Made sure
everything was connected, then continued to drive.

The indicator began coming on consistently every
time I turned on the vehicle, and I noticed whenever
it did, the power steering would go out. I continued
to drive it and muscle through the difficult turns,
until eventually my radio and dashboard began
turning off as you would expect with a bad
alternator. As everything started to die, eventually I
was driving with no power. For a brief second, I lost
gas and had no acceleration, then suddenly the
acceleration came back, and my dashboard and
radio powered back up. Everything just turned back
on, and suddenly I wasn’t getting a Check charging
System indicator anymore and I had power steering
back.

Then I drove through the weekend with no issues,
until this Monday morning (today) when all of the
suddenly the exact same things are happening
again. Any ideas?