If she says, "But I told you that there is no one else." ... Your reply, "Yes, I heard you, but my trust in you is gone. I don't believe you anymore. I need space and time to process my thoughts. If you cannot give me that then I know that you still have complete disregard for me and I have my answer."
I hope you can do the above... and I'd like to hear what other people think of that.
Since you asked for other opinions, I will add mine.
Trust is important. It is one of the four necessary components of a healthy marriage. We need love, commitment, trust, and forgiveness. All four components. Right now, you are missing 3 and one is in question. So we know the patient is not healthy.
I agree with letting her know that she has destroyed your trust. Where I disagree with G is in the demand that she now display the behavior you insist on or you categorically dismiss any attempt by her to reconcile.
This is simply controlling behavior. The lion tamer with the whip and chair, and I object to that in the advice of all the male dominant posters here. I'm not saying that it may not stop the divorce, especially in a case where the wife is already repentant. But it will not heal the marriage. It is untenable in the longterm.
Fine, you can control her behavior now, and prove your "manhood" to the people on this board, but will it lead to a happy partnership with your wife for the rest of your lives? Or is this just going to be some new resentment that she stores in her baggage of hurts and slights through the years. And this baggage tends to become the reason for the next EA or escape technique. To end the cycle you have to really heal the marriage. You both have to throw away the baggage and have a partnership based on love and trust, not fear of abandonment.
Short-term G's advice is fine. Long-term, you need to lose the whip. It will take creative problem solving by you and your wife to heal the marriage, build the trust and commitment, and find forgiveness for each other.