Yes, and yes!
You have to attend the Independent Medical Exam (IME) under California law one time when it is called by the defense attorney in your case (after your case is filed in California Superior Court). Believe, it is not "independent" in any sense of the word, but you are required to attend.

Second part of the answer is "yes," your San Diego injury lawyer can attend your IME. There are some definite advantages for the lawyer to attend too.  You can read about those in the above text link.
Mark Blane
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San Diego Personal Injury Lawyer | California Car Accident Attorney