Oh granite

nothing anyone says is going to change your mind because you are so deeply hurt right now, and i am so sorry for that. It must hurt even more because you knew it was a risk, that she has said she only wants you to talk in therapy-that is what she is trying to break through for you even though it feels painful and like she hates you.
This is what i see as a complete outsider. You are in so so much pain, have come from a very traumatic childhood. It makes complete sense that you are so self-protective: to show any vulnerability equals horrible, awful punishment. I know you can't yet bear hearing words like abuse and trauma, but just from the little you've posted about your mother makes my skIn crawl.
Your T cares about you. I can see it in the way you write about her. One of her boundaries is that she can only do face to face therapy with you, as that is the best way for her to show you that she is there, wants to hear your story, wants to help. That right now, the main problem in therapy is the actual talking, opening yourself to that very raw vulnerability. I know, because i have spent four years having the same sort of problems. My T took away emailing for the exact same reasons: I was definitely more open and sharing of my feelings. And it temporarily made me feel better, got it out of my head for the time being. As my T explained it, sure i felt better for a bit, but it was a band-aid, and i used it as a way of really talking about my feelings-which did not help in the long run.
I know it feels so horrid right now-but i think it was nice she sent a note back. She isnt rejecting you, she is letting you know she DOES want to hear it, but from you. She is letting you process it. It would be worse if she told you in session to read it to her, or that she didnt read it, right? Maybe it wasnt the best way to approach it on her end. Maybe this was an error in judgement, but it doesnt mean she hates you or doesnt care. What i think you should do is go to your session. Bring the letter. Put it in your therapy bag next to your kitty. Write a thread that day asking for pocket riders. We'll be here. Do you know how COURAGEOUS you have been? You keep showing up despite your fears. That means there is a part that desperately needs to be heard, wants to heal.
If you cant read the letter, thats ok. She will know how brave it was for you to show up. If all you can say to her that day is "i am too scared to read it, that is why i mailed it," then consider it a huge feat of excellence! Seriously. If you cant say anything, it is ok.