She really doesn't know what she wants and I believe her answer was an honest one.
You saw that she lied about the cell phone issue until you showed her the hard evidence. It doesn't take 2+ hours to ask someone to take a message down.
She is trying to figure out what love is. She is trying to figure out if love is an emotion and if that's the case, why isn't she feeling it. Sounds like her feelings for you are numb right now and she doesn't understand why she feels differently w/the OM.
Right now, she's not sure if she wants to move out and take a chance w/the OM. Maybe, he's not ready to commit to a relationship and live under the same roof w/her. As long as she is emotionally and/or physically tied to him, she can't be working on the marriage.
At this point, stop trying to rationalize with her. You can't snap her out of this and it is just frustrating you even more so. The more you try to talk to her about it, the more she's going to pull away or even make promises to you that she can't keep.
For now, keep your expectations at zero. If she truly wants to work on the marriage, she would be cutting ties w/the OM and definitely not lengthy conversations w/him. She has to earn your trust and that's not happening at the moment.
No more talks w/her about the relationship. BTW, Your confrontation reminded me of her being a child and you being the authority figure, i.e., father.
For now focus on you and what you need to do for yourself and your family. You can't control her, but you can control how you react/respond to her behavior.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.