Could be a voltage regulator, or maybe even diode bridge problem if it is a voltage issue from the alternator.... To check the diodes just use your meter to read AC voltage at the terminals as they are what turns the AC output of the alternator into DC voltage for the car to use. I think the most AC voltage you should see is under a volt. (memory pending
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But I don't think that is the problem givin the conditions. I would think your best bet would be to have a diagnosis done with the BMW GT1 equipment, either at the dealer or any such equipped BMW specialized independent shop. There is so much more information that may be there that you aren't seeing with the regular scan tool. BMW has its own proprietary fault codes and attached to all faults read through the GT1 are guided test plans to give you any additional information needed for diagnosis.
You may need a new transmission control module, or it could be something else. Best bet is to just have the proper diagnosis done first. Good luck!