She hasn’t given you much to trust in this relationship. She has lied repeatedly, made promises she has broken, and made a conscious, deliberate decision to talk to someone else rather than keep her promise to talk with you. It sounds like she wants you to trust that she will keep doing what she is doing.
Unless I missed it — she hasn’t said that she will stop doing things that hurt you, has she? Lying, breaking promises, and betraying you has been her track-record. Unless there is a specific effort for her to change — it seems like she just wants you to accept it. You are separated because what she’s doing became intolerable. Unless you want to repeatedly get hurt — it is time to move on.