Hi Luke, welcome to MSF!

While I don't know anything about your therapist, her training, or what kinds of therapy she claims to practice, some of what you've said about her sets off alarms for me. For instance:
She seems to have that backwards, in my experience. If she actually does have a valid point there, I don't understand what it could be.

Assuming always that you, your therapist, and I all mean more or less the same things by "healing" and "trust"...

For me, healing and trust seem to be just two different manifestations of a bigger process. As I've worked through whatever might have been keeping me from healing, I've found almost incidentally that I was more willing to trust -- myself as well as others. And as I've worked through whatever might have been stopping me from trusting (myself and/or others), I've found that experience healing in itself. None of that has looked even remotely like, "If you want to heal, then first you have to trust me."

This could very well be just me, but it seems as though the people I've known who seemed the most intent on getting me to trust them ("for my own good", of course) have eventually revealed themselves not to be especially trustworthy. By contrast, the people I've known who over time have proven the most trustworthy, have also been the most willing to let me find out for myself when I felt ready to trust them and when I didn't. I don't seem to recall them ever making an issue of whether I trusted them or not. It was as if they were aware of no reason on their end why I shouldn't trust them. They seemed to assume that if I ever came up with one that they hadn't been aware of, I'd run it by them first instead of straightaway playing "Ha! Gotcha!"
Again, this is just my impression but she seems to be making your therapy (and your trusting her or not) all about her. I imagine her thinking that if she can get you to trust her, or to show signs of healing, or at least to let her try out her novel ideas about therapy on you, it'll somehow prove that she's OK -- or that if you were to choose not to go along, that would be like throwing in her face that she wasn't OK after all. She seems to want you to get better to make her look good.

I can easily picture her wanting to lead you along and allow you as little choice as possible in what happens to you -- because, what if you were to choose something that didn't help her see herself as the great therapist she wishes she were?

I'm not in any position to advise you to distance yourself from this therapist as gracefully as possible. That's what I'd do in a situation like that, though.