I think she already has ended it. There's probably no way you would ever really trust her again. For some reason she's stalling about initiating divorce. You can pursue that without waiting for her, though you don't have to. You could simply hang back . . . not hoping for what's beyond unlikely . . . but just because no law says you have to do anything.

I was looking up legal separation, and, from what I read, I don't think it would accomplish anything better that what you already have, which is an informal separation. Here's the article:

Benefits and Disadvantages of Legal Separation (vs. Divorce)