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There are some simple things that can cause rough idle like an air leak, bad crankcase vent valve, bad temp sensor, or leaky injectors.
Unfortunately your symptoms fit the symptoms of bad levers 100%, so that is most likely the problem.
Here is the BMW bulletin on the issue: CLICK HERE TO VIEW BULLETIN and then press "download" to save a copy to your computer.
The dealer mis diagnosed the issue, you need to have the levers replaced. Your sympoms fit this problem 100%.
This is VERY common and is your problem for sure, exactly as laid out in the bulletin I have provided. I would suggest the dealer cut you a HUGE deal on labor for the proper repair, since they have already spent a lot of your money on a wrong diagnosis.
I hope that is helpful, please let me know if you have further questions, or if I can clarify anything for you.
It has been my pleasure to help today and I wish you the best of luck with your vehicle.
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thank you in advance.