Hi Nick
I would email to them first outlining your concerns regarding the fact that (1) They seemed to have problems diagnosing the issue first off (2) After further investigation they provided a repair which is not satisfactory.
Point out that this has reduced your confidence in the reliability of the car and their ability to maintain it, ask what action they will take to rectify copy BMW UK Customer Services (you do need to give them an opportunity)
Then go and see them let them explain the course of action they intend to take. If you find it unreasonable escalate your complaint explaining that you have spent good money with them but they have not provided goods that are "fit for purpose" and you require them to repair or replace them in a timely manner, if they cannot then a full refund would be your only recourse.
By doing this you will have a record of what is happening that is a legal document should things get bumpy. Dealers vary, my local dealer is very good efficient and helpful, I used a Dealer 15 miles away and they were the absolute pit's. The Service Manager was arrogant to the point of rudeness. so sadly we pay our money and take our chances.
I am sure they won't let it get that far
Good Luck
Dave