I think it is human nature to assume that other people think and react to things in the same way that we do. One of the reasons many of us got away with our infidelity for so long is because our spouses couldn't imagine that we'd react in a way that they wouldn't. If some guy suggested to my wife that she cheat on her husband, she'd punch him in the nose, because she has way too much respect for herself to even consider such a thing. At the time of my affair however, when offered the same opportunity, I made a very bad choice. I did not respect myself or her enough to say no.
During the affair, and even for quite a bit of time afterward (I really, really got stuck in my wayward thinking patterns for the longest time) I kept expecting my wife to do similar to things to me that I had done to her. I expected she was "out to get me". I worried that she was out looking for a revenge affair. During the affair, there were times I wished that she WOULD cheat, just so I could feel better about my own actions and to remove any doubt from my mind. When she asked me to separate our bank accounts I accused her of trying to destroy me financially. When she asked me to enforce boundaries with our kids, I thought she was trying to get them to hate me and love her instead. When she asked for a prenup I accused her of just wanting to punish me for the affair. My point being, everything that I had done to her, I was accusing her of doing to me, because I expected her to react to things the way I do. And in every single case, I was wrong.
My advice to you is to take this as a teachable moment for yourself. This is an opportunity to turn this situation around and use it to rebuild empathy within yourself. As you said, you don't like how it feels to be on this end of the infidelity story. She's shown you the texts and made it clear nothing happened, and yet you can't get over it, can't get it out of your head, can't just trust her to do the right thing, but more than anything however, you are thinking about yourself, your feelings, your hurt, your concerns, your needs, and her... nope. You aren't thinking about her at all. She's not even in this story you wrote except as someone who is causing you distress. Your insecurity is paramount here, and you don't like being put into a position where your feelings are not being considered and where you aren't in control, at all.
Take this opportunity to turn this around. Rather, ask yourself how SHE feels in this situation. What does SHE need to feel safe and secure? What was it like for her to find out what you were doing in secret, behind her back? Right now, you are thinking almost the same as someone who punched someone else in the face, and then got very upset that the other person wasn't sympathetic to how much your hand hurts after punching them. Do you understand? Understand this... whoever this guy is, even if she barely knows him... she still trusts HIM more than she trusts YOU right now. Because he never betrayed her, or lied to her, or even so much as gave her crap for being married to you. Do you know what that dude has that you don't right now? He's listening to her. He's paying attention to her. He's not judging her and he's not asking for her to care about him in any way. Rather, he is offering her a friendly ear, a shoulder to cry on, empathy... understanding... and wants to be there for her, to help. Sure, he's probably just trying to get in good with her, but put that aside for a moment, because it doesn't matter. What matters is that he is giving her what you cannot, what you will not, and what you are not.
You are here, on SI, among friends, who care about you, and her. You tell us your feelings, your secrets, your hurts, your hopes... these things help, don't they? I mean, at least you have a place to go and people to talk to, can get advice, or comfort, or the occasional ass-kicking even, but we are a support system for you. What about her? Who does she have? Who can she talk to? How should she find comfort? To even talk about this is hard, and in doing so, she probably feels that she is exposing to the world how she got duped and used and dumped. Wouldn't it be awesome if she could talk to YOU about this? She could, if you could be there for her. Right now, you are too worried about yourself, and too worried about trying to control the outcomes, to be there for her. In Brene Brown's terms, you are "hustling for your worth", and that doesn't help her at all, it just makes things worse for her actually, as it diminishes her even more.
If you want to dissuade her from going to other people to get her needs met, then you need to be the person who can meet those needs for her. And until you are, she needs to have the freedom to do whatever she needs to survive, without having to worry about your approval. Telling her who she can not have a relationship with is not a good start, especially when you never followed those same rules yourself. Double standards and all.
This line of thinking is what is preventing forward movement at the moment. Stop trying to do the right thing, the thing that will make her happy with you. You are looking for her approval in order to feel better about yourself. Instead, do the right thing(s), because being a good, decent person is all about that.
“When we can let go of what other people think and own our story, we gain access to our worthiness—the feeling that we are enough just as we are and that we are worthy of love and belonging. When we spend a lifetime trying to distance ourselves from the parts of our lives that don’t fit with who we think we’re supposed to be, we stand outside of our story and hustle for our worthiness by constantly performing, perfecting, pleasing, and proving. Our sense of worthiness—that critically important piece that gives us access to love and belonging—lives inside of our story.” - Brene Brown