Ditch:
I think your dealer has not kept in the "Loop" as to the problems that have been discussed in MINI sites, "Ad Naseum".
There have been a "batch" or Coopers (5 speeds and CVTs) that have come with defective engine wiring harnesses from the factory. In some others, the cable connection to the throttle body control module is defective, hence causing the EML light to come up (Causing the car to go into "Crawl" safemode) or recurring engine stutters and stalls.
If your dealer has any hint at servicing these cars (And I am sure there are MINI issued service bulletins on the subject), they should have already replaced the engine wiring harness and the throttle body control module as the first steps in isolating the problem.
Secondly, you need to make sure that your car has software update 33.2 installed in the DME. If your car already has 33.2 and still shakes, hesitates and stalls, then one of the above 2 culprits could be causing the whole system to crumble.
My car was built the first week of August 2002 (Last batch of the '02 model year) and hence was not part of the infamous CVT tranny oil recall. There has been talk that cars that came with the wrong oil from the factory could have already sustained long term transmission damage. Just think for a minute....how many miles did you drive your car before finding out that the transmission had the wrong viscosity fluid in it? 500 miles? 1000 miles? 5000 miles? Enough time to create damage downthere without you even knowing it.
Some owners (Poster Technomage comes to mind) were succesful at getting MINIUSA to buyback and replace their troublesome early 2003 production Cooper CVTs. he had the same problems you had and after attempting every fix in the book the car never drove right. He know drives a new '03
MCS (He is out in California I think).
My suggestion would be for you to call MINI Technician, Franz Laman at Lauderdale MINI in Ft. Lauderdale, FL. This guy is extremely knowledgeable in all MINI service related matters. His phone number is (954)763-4777.
I'll let you know about this weekend as I have a few commitments going on. I'll send you a private message later today.
Best of luck.