I agree that you should be as honest as possible with your t. Therapy should be directed by the wishes and needs of the client, not the opinion of the therapist.
Speaking only from my own experience, (this probably does not apply to your situation, but is related and may be helpful to someone reading) I started trauma work with a trauma therapist without any knowledge or discussion of parts whatsoever. The result was an uncontrollable overflow of flashbacks, depression, dissociation, and the return of old addictions. The trauma work punched holes through the dissociative barriers between my parts and I, and one of them confronted me (to my shock) and told me he would interrupt the next therapy session if this continued, he said, because I would not be able to handle the memories that were about to surface. He was protecting me, and he was right. I tried to continue the trauma work anyway, though more carefully, but more parts surfaced and confounded my efforts. In my case I have learned that trauma work is essentially work with parts, because they carry the trauma memories. I didn't want to believe I had parts, or that I had to understand and learn to interact with them, because I wanted to just "get better." Also I was fearful and distrustful of my parts. I have another therapist now who specializes in dissociative disorders, who has helped me to accept my parts, understand their functions, and is teaching us to care for each other. I never want to go back to the way it was before.