EMDR is a two part course. The first two and a half days of training is called Level I and the second two and a half days is called Level II. It's just the same as saying part one and two. All clinicians need the information taught in the full course.
There are consultants available in the specialty area of treating dissociative disorders. I have posted these consultants previously. They can be accessed through the EMDR Institute at inst@emdr.com.
You might suggest that your clinician try another form of bilateral stimulation during your processing. For instance, you might find that handtaps might be preferrable to the eye movements.
I urge you to discuss your concerns with your therapist.