I think she needs to feel free to make choices about her life. If she feels traped and sees no way out of a miserable existence, then it could cause her to be more depressed. However, I don't understand why she wouldn't just leave to be with OM. Is he M with kids? Why is she still living with you? Usually, the OM is seen by the WW as an escape route for her dreary life.
Maybe she sees this as you not cooperating and more of your controlling behavior.
I don't think it is wise in every single case to refuse to cooperate. It doesn't mean you want the D.
If my S wanted away from me bad enough to threaten or hint at suicide, I believe I could let him go.
IDK, it may be a trick, but I would not call her bluff. I mean......who would want to live with that type of responsibility, to think she'd see suicide as her only escape.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!