First off, have a hug:

I know this must be really difficult and upsetting, especially given you have really painful wounds where abandonment is concerned. I know from my own experience that any mention of leaving therapy or of your T not being able to help can start those alarm klaxons. I'm always criticising my T (he thinks I'm trying to break down his authority as authority figures are scary and hurt me, he's probably right) but once he said: "Maybe I am inept, maybe I'm not the right person to help you," and I was FURIOUS. I didn't want HIM to say that.

I think email is always problematic because tone of voice gets lost. I also think it would be an idea to say to your T that, whatever she thinks is true, YOUR experience was that she said this. That is your truth, and I think it would be more helpful to look at what you experienced and how you felt about it, rather than her debating over what she said.

I did notice a lot of I-feel statements in your post, though.

Am I wrong in thinking that she is having doubts about our work together, and wants me to go elsewhere?

I think it's worth clarifying that you believe or feel this. Your feelings can't be 'wrong', in that they're information about how you feel, but they don't tell you what's actually going on with your T.

I don't think she's angry. I think her email sounded rather abrupt, but that's the problem with email, it can sound that way when perhaps it's not meant to. I'm just remembering a time recently when I texted my T because I was angry and he sent me this message back saying perhaps there was a misunderstanding that needed to be cleared up. I was absolutely convinced he meant he was going to terminate me, and actually we had the loveliest session ever.

I do think your T sounds abrupt, and it's worth talking to her about that, and about your experience of what she said. But I don't think she's angry.