There may be some confusion and some differences of opinions. First, you appear confused about what to do b/c you don't know if you are piecing or not. Here's how I look at it.
The WW has to agree to the H's terms (Tell OM it's over,it was a terrible mistake, she loves her H and wants to work on her M. She ends all contact with OM forever. She agrees to follow the transparency plan her H designs,) She may not feel remorseful at this point, but it is more important that she agrees to the terms and cooperates. The H should explain to her that she will experience strong symptoms of withdrawals as she faces the next few months, and it is important that she understands that being transparent not only helps her H feel more secure, but it helps her to stay on track as she goes through the affair withdrawals. He can also explain how this transparency plan will not be a requirement forever, but for a while her honesty and faithfulness is on the line. (Don't give her time limit.)
IMHO, the period of time the WW is going through her affair withdrawals, is like a bridge to piecing. If she can't get over that bridge, then "piecing" will be fake, and she'll continue having a secret life apart from the M. She may experience depression, insomnia, etc. She may not. It is a difficult thing to get through. It took me four months of hard withdrawals, and then I went through a lot of depression, etc.,.......and I had never met OM in person. This is why I try to emphasize that it is about the fantasy. If she will kill the fantasy, then their is a high probably of having a good MR.
This leads me to her responding to OM's email. Your W and this OM have a shared goal, and it's pretty specific. They plan to wait till their youngest kids turn 18, and then they'll go be together. Do you know what this shared secret goal does for her? It keeps the fantasy alive! Every time she contacts OM or responds to his contact.......it sets her back to the starting line again. Whatever ground she may have gained, will be lost and she'll have to go through those withdrawal symptoms again (if she even went through any at all). It prevents her from truly loving her H the way a W should. It cheats both of you from the relationship you could otherwise experience.
I want to point out something else that I think may be an area of confusion. Your job in the transparency operation is to give her moral and emotional support, encourage her, and...... monitor her activities, especially the messages. She agreed to the transparency plan. It has nothing to do about your "need to snoop". I wish you would get that out of your head. She has to prove herself, and has invited you to look......and you are telling her that you're good and don't need to look. She needs to be accountable, and you are telling her it's not necessary. Yes, it is necessary, otherwise, she won't get through this process. The MR is reconciling, and she's going through withdrawals (hopefully), and that puts the relationship in different status. I think I talked to you once before about the 37 rules and how that changes for the couple who is reconciling/piecing.
The last thing I want to remind you about is your boundaries. Do you have a boundary about her continuing contact with OM? I know one thing you didn't do. You did not insist that she send OM the message about ending the affair. You let it slide. Now, you've discovered one deleted email from about three weeks ago. So, my question is how many times does she contact/respond to OM before you enforce your boundary?
There is plenty of other things to exercise patience. I just don't believe this is one of those things. It is critical that she knows she cannot get away with hidden messages to OM. Your passiveness wants you to turn your head and not say anything about her breaking her agreement to be transparent.
Like many other LBH's, you thought her withdrawals would be over in a couple to three weeks. I think Steve's sitch may have broken a record, IDK. It was pretty quick......and yours may be quick once she realizes you aren't going to play this game with her. There is so much emotional stuff she has to work through, and so it's kind of difficult to know where one issue is resolved and the healing of another begins. The H can't force her through the process, but he can influence how serious she gets about her efforts. Once she really sees what she will lose......she can get real serious about doing the work to save her M. The H can stick by his boundaries. He can require her to give accountability when lines have been crossed or there is a question about anything. So far, all I can tell about her is that she's apparently showing you some type of emotion that resembles remorse., and apologizing. It may be an act, but I hope it's genuine. I have to wonder since she refused to tell OM to get lost, and she broke NC early into this reconciliation period. .
It's your decision as to how you want to handle things. If you decide not to tell her you know about the email, then I strongly recommend you monitor her much closer in the following weeks. If NC is broken again, you have to address it........or otherwise what is to gain by turning your head and giving her a pass? See what I mean? This entire process is to help her through the affair withdrawals. Not addressing it doesn't help her.
Getting through the affair withdrawals is first.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!