Glad to hear you got it moving.

Someone in parts and/or that SA is simply not doing a competent job...the people you called that located the alternator used EXACTLY the same tools that your dealer has at their fingertips.

That really is inexcusable.

So BMW had a recall for this precise issue...you should file a complaint with DOT stating that BMW failed to properly identify the affected cars in the recall as yours also failed. as someone who has run a few recalls, there is nothing worse than telling regulators "we know what the issue is, what is affected and what the solution is"..then having to say "oh, whoops"

Here: https://www-odi.nhtsa.dot.gov/ivoq/

It may help others too.

GL- may you be back in your car this weekend!

So now you're doing the leg work your dealership should ! Wow. I can not begin to tell you the stink I would've raised by now. Hopefully you get your vehicle back soon.