@Beachbeachbeach,
Welcome to SI, you've received some excellent advice so far, and it is good that you are taking it to heart. It is also good that you are open to suggestions, even when they are scary and uncomfortable. And trust me, everyone here, no matter their story, knows those two feelings.
The thing about not confessing is that it removes the choice and the dignity of your spouse, and from yourself. You have all the facts, he does not. Yet, you are making choices and decisions for him right now, this very moment, based on your own needs and your interpretation of his needs. You are stealing his agency, and even though the affair may be "over" (and even that isn't 100% true right now) you still carry the lie of omission every single day. You lay next to him at night, and he loves you, trusts you, believes you have his back and his best interests at heart. If he did know these things were not true, he may not be okay with that. He still thinks you were somewhere else, doing something else, when you were with your AP. He is living a lie, and you are actively making sure he continues to live that lie. That is not love, it not compassion, and let's be honest, that isn't "saving him pain", that's saving you pain. It isn't humane. You are being more honest with us, a bunch of strangers, than you are with the man you swore to love and honor and protect. He is robbed of the most basic rights a human has - to make his own choices and decisions about who and what he wants in his life.
(OH, and he might have once said, "I don't want to know", but then again, you once said you would love him and be faithful. Sometimes what we once said when not in the midst of betrayal can change.)
Now, a lot of what I just said may feel very "Attacky" right now, and I apologize for that harshness. Please know that it is not my intention to attack you in any way. The very nature of infidelity is harsh. I am a WS too, and a really, really shitty one at that, and caused my spouse, and my kids, SO MUCH MORE PAIN than necessary because I couldn't see past my own fear and pain enough to see and feel theirs, or to honor the dignity they deserved from me. In the end, while the affair was a horrible thing, the lies and the betrayal were the worst things for her. She now is forced to look back on everything, not just during the affair, but our whole marriage, and wonder what was a lie, and how else was I betraying her in life? She felt kicked the curb, used, played for a fool, and do you know why she felt that way? Because that's exactly how I treated her.
The reason I'm being so direct and harsh, is because I want the message to get through. I needed folks to be this honest and assertive with me when I was new here, and even then, I didn't "get it" for a long time. I was once in the "It's my shame, not hers, why make her carry this burden yada yada yada" camp as well. Now, in the aftermath of everything, I realize how very much that was still self-protection on my part. All affairs start with justifications and excuses for what we know is wrong, but we turn things on their head until they fit the story we want. That's how the affair happened in the first place. And now, it is how it is covered up.
End soapbox on confession. :)
Regarding the AP, this too is something that needs to be examined. As you said, he is married, to a woman he loves, with kids, and yet seemed awfully comfortable with having an affair with you, and is still comfortable with asking you for sexts. What part of that sounds like someone you should be unable to start dreaming about, or want to marry or have kids with? He doesn't love you, he certainly doesn't respect you, and he is making it very clear what he wants from you. It isn't love. He just wants to see your tits. Is this a prince? Is this someone worth throwing away a marriage over? Is this someone worth throwing your dignity away over? You deserve better. Your husband deserves better. His wife and kids deserve better. He's handsome, charming, scum. Don't lower yourself to match his value. Rise above. As you said, even saying the truth here, offers some relief. I know you might not think so at the moment, but when the affair is disclosed and dealt with, the weight of it all drops. It honestly feels like a ball and chain were removed.
The way you get over your AP, and the way you attempt to fix your marriage, are the same. You need to figure out what the heck it is you really want, and why. The AP still fills some sort of need for you. Maybe he represents an escape for you, or maybe he makes you feel special or attractive? Maybe there is something about you that feels you aren't deserving of your husband's love for some reason, and the love of a cheater is more in line with your self-worth? (That was one of my big reasons). Whatever it is, it is unhealthy, so figure it out and deal with it, for everyone's sake and well being.
I am going into year 5 of R with my wife now. As difficult as it was at the time, I am thankful for the people who steered me in the direction of becoming a better person and of taking accountability for my actions. Working through R together can be a boon to both spouses. She has the whole truth now, all of it, and she makes her own decisions about what she is willing to accept in her life, and what not, and why. I no longer carry the burden of the big lie, and the self-respect I have gained through this process is enormous. I will never be proud of what I did, and cannot forgive myself for the permanent damage I caused. But being accountable for my deeds makes it easier. I know that today, I am a safer person for my spouse to be around, for my kids to be around, for anyone really, if for no other reason than now I have healthy boundaries, self-respect, and empathy that did not exist during the affair. I do not live in fear of being found out, she does not live a lie. It has given us the opportunity to know ourselves and each other better, and in that, we actually have a stronger relationship, because it is based on vulnerability, authenticity and truth.
As others have said, first, end the relationship, permanently, and under no uncertain terms. Then, tell your spouse everything, no "trickle truth", just lay it all out as best you can. Give him any emails, sext photos, texts, whatever you have. Throw yourself under the bus. There is no "good time" to do this, it just has to be done. He may leave or kick you out, this is a possibility, so be prepared for it. Hopefully however, if you take accountability for your actions, and recognize his pain, and are willing to sacrifice anything to save the marriage, maybe you'll be surprised. This might be the end. Then again, it could be a new beginning. Don't cheat either one of yourselves of that possibility. We cannot be accountable or become safer, more honest people while continuing to lie and manipulate things to our own ends and desires. Good luck to you both, and please, keep coming back. There is so much experience and wisdom here, from people that have walked in your shoes, and walked the path that yet lies ahead.