This really is a difficult situation and frankly, I'm not surprised it raises so many and so different opinions... so here's mine

At first, I was also feeling like the T might have overreacted- most ppl do punch stg inanimate when they're angry but still even when I thought she did overreact, I believed she had every right to terminate. Once the T recognizes he/she can't work with a client for any reason, isn't it better (even for the client) if the T terminates? I don't think Ts ought to have thicker skin or whatever, and/or that termination speaks about their capability/expertise. (The way she did it was a bit weird though...)
However, from the OP's later post- about the OP choosing to intimidate her to get what he/she wants... yeah, that did not sit well with me and I do think even many Ts will have a problem with this particular coping strategy...
It's great that the OP realizes that this is not working for him/her and is willing to work on it. I think maybe being open with your new T from the beginning will help- good luck.
BTW, I would send the apology mail anyway, would help me feel better about this unfortunate situation and I would hope that the T might feel better too.