'03 LR Disco II, 103,000k. A month ago, battery went bad. Autozone tested battery and alternator and said alternator was fine, but battery was dead. Bought an Optima battery and replaced. Afterward, battery light would periodically come on, then go back off. Thought the connections to new battery were loose. Then, after a couple weeks, the car just shuts off while driving, and all the dash lights are going nuts. We got a jump, and drove to Advance Auto Parts uneventfully. They test battery and alternator again, and tell us alternator is bad. So, one tow home, and $300 later, my husband installs a rebuilt Duralast alternator from Autozone. Battery light has not come on again since, but the new alternator makes a weird, high pitched whine all the time. Is this something I should be concerned about?

 

Yes, take it back to the zone.

 

Dump the cheap rebuilt alt and buy a brand new one from them.
I went through 4 rebuilts in 2 years and settled on a used one which has lasted longer than any of the rebuilts that i got.

The bearings are bad in your "new" alt.
They only replace what is bad when they come in to the rebuild factory.

 

I agree, their alternators are junk, I would order one from British Parts of Utah and then return the noisy alternator for your money back.
When that is all done, have the voltage checked sometime, should between 13.6 and 14.4 volts.