Do I encourage this? Or do I tell her that I don't trust her? Demand proof? I'm at a loss.
The "demanding proof" part will come later, IF and WHEN she is sincere (which I doubt she is, btw, but I could be wrong ... if she is, waiting won't hurt anything, and if she isn't, waiting is absolutely the way to go). At that point, you can lay out what no-contact letter and full transparency plan look like. For now, this is a woman who has cheated on you and LIED ABOUT IT for 2-3 years, including going to be with her OM to have sex with him when she knew that YOU knew she was going to at least see a man with whom she admitted she had an AE with. She's trying to take your temperature, and frankly she doesn't deserve any answers from you right now. It's not your job to make her feel better about bombing you last nite, and cheating on you for 2-3 years.