taking a more newer BMW to a general mechanic is like taking a medical problem that needs a specialist to a GP. You DON'T do it. These cars are very specific and require this type of attention. I suspect the shimmy is poor balancing and possible control arm bushings -not uncommon. However, in fairness, not even BMW tech can know and sometimes they guess and not always get it right. I've seen it, worked with them too. as mentioned it helps to be knowledgeable to a degree about these cars as you can help yourself whether to take to a reputable shop.
I once took a bmw to get painted. I got a decent quote but when the car was finished it was a horrible job. I realized what HE thought was good wasn't so clearly he wasn't a professional. I wanted my car out of there after 3 weeks so I went there and used their space to water sand and polish -2 more weeks as I worked at the time. I learned my lesson; would I go back..? I ran for the hills. NEVER! lesson learned.
as said, consider it a learning experience and from here on in you'll probably save yourself a lot of money in the long run going to a reputable shop.