You have been a kind, patient, understanding and accepting man. My conclusion though is that it is now time for the gloves to come off. Let's look at the very basic facts. She continues to lie and contact him. You ask her questions and she always lies. Please don't even bother asking her the questions anymore because you are wasting your time, right? This is not reactionary, I have been there. My W tested me on just what I would tolerate so I showed her. I didn't continue to be accepting when I couldn't accept her behavior. I didn't keep secret my covert knowledge, I exposed her. Was she happy? Not in the least but you don't have to scarifice your standards because she is. The D threat was needed and will probably work for a while. Yes, for a while. She just keeps lying and deceiving. Even her words and actions towards you are deceitful. My W was especially affectionate and sexual while she was on match.com everyday for hours at a time. She wasn't about to abandon the current ship until the new one was ready to go. That is one rule that women cheaters seem to follow. The men will chase the A without securing their current sitch. Men seem to focus on one where women tend to share their "love".
She can't let her A go so maybe you should encourage it. Ask her to leave. I told my W that any "pursuit" behavior would not be tolerated under my roof and if it did her things would be on the front porch with the locks changed. I told her that she is free to do what she wants on her own but not here. She asked me why I didn't leave. I said that I am not the one that wants out. You have been a confronter during this whole sitch and that is good but follow-through is necessary.
Please keep an eye on the depression, been there too. Take care of yourself and your children. Don't waste your time with more advanced snooping. It is a complete wast of time. She will just try harder to not get caught and now you made it a "game" and you won't win.