I'm speaking to you as someone who was formerly a disloyal spouse (in other words, I had an affair). I'm going to speak to you not from the point of view of a spouse who has been betrayed, but from the point of view of the one who did the betraying, okay?
Right now, chances are about 99.99% that he is in "Cover Your A$$" mode. He knows that you know. He knows that what he's done is wrong and made a mess. But he's hoping that if he only give you "a bit here" and "a bit there" he can get away with minimum consequences and maybe convince you to stay so he can have his cake and eat it too. In other words, maybe the OW boosted his ego and complimented him and made him feel great...but you met some needs too like free childcare, free housecleaning, or additional income AND he also had a convenient scapegoat: YOU! He doesn't want to have to face the results of his choice to be a cheater because they hurt. And he doesn't want to lose the needs you do fulfill--whatever they may be--because if you weren't around who would he blame for the $hit in his life? It couldn't possibly be HIM!
Soooo...in order to keep you on the hook and minimize damage, he'll feed you just enough to say "I KNEW IT!" (because you know some...but not everything), and he'll hold back just enough for you to doubt yourself. He's doing this for SELF-preservation, and I want you to look really closely at that word. WHO is he preserving? You? NOPE! HimSELF. It's all SELF-centered.
Almost no adulterer I know thinks to themselves that the natural consequence--the result that comes naturally--of flirting and cheating ... is LOSS OF THE MARRAGE, and loss of half of everything they own, and loss of half their time with their children! No one thinks of that. They just think "if they don't know it won't hurt anything" and carry on, right? But IN REAL LIFE every choice has both a benefit and a cost. The benefit of cheating is that huge ego boost! You feel ALIVE and interesting and great! But the cost (the result) is exactly what I said: a nuclear bomb is dropped on the marriage and family and it is no longer alive anymore.
Now, the cheater may think "If I minimize it can go back to the way it was, and I'll feel good again." Or the loyal spouse may think "If they just grovel a little and tell me how sorry they are, it can go back to the way it was." But that's not true. As of right now, this moment, your former marriage IS DEAD. It is gone. You can't apply pressure and do CPR and "save it" because it is DEAD. There's a piece blown up over here...another piece over there...several pieces up on the roof...and it is blown to smithereens.
In order for there to ever be a marriage again, you and your disloyal H are going to have to rebuild from the rubble. And for rebuilding to even start and be a possibility he would need to have a fundamental change of heart and change of approach: going from SELF-centered to SPOUSE-centered.
I'm not saying you were an angel before the affair. I suspect you had become busy with life and bills and work and kids and school and kind of let the marriage slide, unintentionally. People often do that with no bad intent. I bet you didn't treat him like a guest (politely and kindly) and started to become irritated with his habits that drove you nuts. See these are the things that an unrepentant disloyal often bring up as reasons for their affair, and the loyal will say "Well...I did kind of do that, so maybe they have a point." NO!
Let me say that again: NO!!!!!!
Even if you were yelling about socks on the floor and not paying attention to him, the solution to that is NOT to choose to commit adultery and then blame it on another!! There are hundreds of solutions that are moral options that show stronger character than choose to commit adultery. And when he calls it "a fling" or "I slipped"... no he didn't. That's just a euphemism. He committed adultery!
So the natural cost of committing adultery is losing your spouse and family (and half your stuff). THAT is what he is due. And the very first step of any recovery will be when he recognizes...really understands in his heart...that WHAT HE DID resulted in the death of the marriage and he is due NOTHING. He is not owed a second chance. He is not owed "forgiveness" nor "you getting over it." He is OWED losing his wife, half the time with the kids, and half of everything he owns. If--someday in the future--he does NOT get that, then it is an amazing gift that he should never, EVER take for granted!!
Once he really understands in his heart that his actions KILLED the marriage and family, the next thing that needs to happen is for him to shift from "protecting himself" to "doing whatever he can to save you." In other words the shift is from SELF-centered, to SPOUSE-centered. When his attitude is "I do not deserve a second chance, but that doesn't matter, because I see the harm I've done to you and my own children and I'm SICK. Even if we don't reconcile I need to do everything I can to help you recover from the damage I did!" then you'll know that he's made this switch. Until you see that kind of attitude from him, you really can not rebuild anything that will live and be healthy.
This is why we so strongly recommend that a disloyal spouse talk to HIS parents...and HER parents...and admit what they've done and ask for forgiveness. It's not to force them to go through certain motions. That's robotic! Nope, it's to demonstrate in a very active way that they understand their damage didn't only hit the spouse and kids, but also the grandparents, the aunts and uncles, the friends like ripples in a pond. It's to demonstrate that change in focus too. By talking to parents willingly, that demonstrates "I'm not trying to save mySELF but rather I'm focusing outward on the people I hurt."
So are you seeing that kind of change in attitude? Be honest--are his ACTIONS protecting HIM...or protecting YOU and the kids? Don't listen to his words--at this point they are hot air and worthless. But ACTIONS--actions will tell the truth. What do his ACTIONS show you?