I am glad you emailed her, although I am not sure she will be able to hear what you are saying because so far her response to when you reach out is to back away.
There appears to be some push pull happening here between you and your t. You are acutely aware of it but your t is not owning her part in it. She even admitted to backing off. I wonder if she is in therapy herself or supervision because she really needs to look at her process. Perhaps she is being triggered by her own inner child work.
Anyway that’s about her but do you recognise this process of being vulnerable with someone only to be pushed away or rejected? It could be stirring up some very old wounds of yours.
I wonder do you feel safe with this t? I would find it hard to work with a t like that.