Hopeless - You're not hopeless. Everything that happens leads to another experience and so do all our choices. This may seem like the end of the world, but it's not....it's the logical outcome of many choices that you have made over time. I don't say this to blame you, you know what you've done, but to encourage you to take responsibility for all your choices in this relationship in the past and going forward. You have agency, you're not a helpless victim of fate, and your husband has agency too, to do what he wants. While you both will probably try the best you can for your children - he doesn't owe you personally anything at this point and I don't know how much you can do right now to make it better. But whatever happens next, it's not the end of the world, learn from it and grow and be a better person. You KNOW what is right and wrong, you have to live up to this and hopefully teach it to your children.
You've had a lot of excellent advice here and I may repeat some things you've already heard. I would urge you NOT to put up any stop signs because while Waywards can give you support, the Betrayeds will give you the best understanding of what you have done, what the impact is, and how this may end....which can be in different ways. So please be open to it even if it hurts, sometimes the best medicine is unpleasant.
Here's the biggest red flag in your story for me. Whenever I hear that someone has been unfaithful during the start of a relationship - during a courtship - and then during a wedding.....I have to believe there was never a real marriage in the first place. Which is probably what your husband thinks. It sounds like the guy you REALLY wanted was the other guy, your AP, the one you invited to the wedding. I think that was an unconscious decision to put him in an approximate relationship to the GROOM. I think he's the one you wanted. Let's be honest. I've been in love several times before my husband, I've always been a sucker for love, but I never cheated on these guys....I've never cheated on my husband, possibly because of integrity....but mainly because I didn't want to as I was IN LOVE WITH THESE GUYS. And you don't cheat on someone you are really in love with. People in love don't cheat during their courtship, because you are besotted with each other, or should be, and same with the marriage and the whole honeymoon period. That's normal behavior. Sometimes the cheating starts with having kids, but up to that point, it should all be stardust and moonglow.
You don't seem to have felt this way about your husband or you would not have taken up with this other man at that time. And you would never have invited him to your wedding. It's not only that you were not in love with your husband, that's gross disrespect. So I figure for whatever reasons - they could cultural or economic or fiance seems like the "right type" or whatever....you decided he would be a good Plan B to have a marriage and family with. Stable, reliable, probably in love with you, good man, trusting, etc. And maybe Guy Number 1, the one you really wanted, didn't have those qualities and didn't work out. This IS what I think about your cheating on your husband at that point, which to me is a sure sign....you should NEVER have married him. This is probably what he thinks and he's right to think that.
You have to be honest about why you would practice that very basic level of faithlessness and deceit upon a boyfriend, a fiance, a brand new husband. Why didn't you love him enough to be faithful? For a year or more? So you need to start asking yourself those questions because that's where your problems with him start. Why did you marry this guy -honestly....and wouldn't you - at that time - really have preferred the other guy? BE HONEST ABOUT THIS because it's important to understand why you did this and made these choices. My mother made a bad choice too....her fiance died tragically and left her just broken. Broken over it. She met my father I think the same year and he pursued her and she unfortunately married him, and they lived unhappily ever after because she was not in the right mind for marriage and she wanted to get married to just about anyone because she was getting older and wanted children and some kind of stability. I suppose these kind of marriages can work if both people have the proper understanding of them, the same starting point, but if one thinks the marriage is based on love, and the other thinks...."he's okay", that's not gonna work. At some point the mirage breaks down. Took you some time, but it did break down.
I don't know why you cheated with the 2nd guy - for a year, was it....again, why do this? You have to understand yourself first. Was it perhaps a continuation of the first affair - did this guy remind you of the original AP. We often have "types". Were you bored with marriage? Were you sick of your husband? Were you thinking is this all there is? What was going on with you?
The whole thing of revealing this to your husband amid all your relatives and friends and the police is absolutely disgraceful and you don't seem to be taking responsibility for this. It's bad enough to be unfaithful in these ways, especially THE FIRST GUY which basically was a denial of your marriage, but to bring in all these people esp the cops on top of his head when he is dealing with the biggest shock and betrayal of his life is astounding. It feels like a sandbagging. I have to wonder if you have some unconscious anger or hostility towards him you might want to explore. No wonder he wants a divorce, I WOULD TO. And in fact, I think he should get a divorce. I think it's the only way you two are going to get clarity, because I think if you stay together, you're going to try to cover this up, love bomb him, explain things endlessly without real explanations, and you can't until you can answer WHY YOU WOULD CHEAT ON YOUR FIANCE AND HUSBAND WITH THAT FIRST GUY? And he would only stick his hurt and resentment and anger and lack of trust deeper inside....probably for the kids and....that is no way to live. That's a half life.
He can't understand why you would do this, most people can't. The logical assumption is that you never really loved him and that you married him for some other reason, whatever it is. He didn't know that, probably didn't really suspect it. And now he finds out his beautiful wife (whatever you look like a believed spouse is always beautiful) has shared the most intimate things with another man and invited him to the wedding. It's a negation of the marriage itself. That's what it feels like and it's very hard to work around that. It makes it seem like your 14 years or so of marriage was more like a job you undertook. It makes him see you differently and that can't be avoided. He doesn't know who you are anymore.
I think he should be independent from you for a while, you two can figure out co-parenting and you should be good to him in any divorce and I would not bother with recon at this point because this is the kind of thing that, IMO, only time can heal....time and distance help to create perspective. You have to know why you did these things to have fruitful discussions with him.
Maybe you really DON'T love him like one should with a husband - you may discover that, that's okay but just trying to recover what was before he found out the truth.....time doesn't go backwards. He knows and he'll always know, this is part of you, part of your history together and IMO, he has to have time and space to work this out.
You may eventually end up back together, I don't want to put that out as hope because I don't think that's what you should be striving for. I think you should be striving for self knowledge and understanding that hopefully you can pass on to him. And also....don't make him look bad to anyone else, like relatives or friends or work etc. This is something you created and you have to take responsibility for it and work your way through it. I think that's your job going forward. Be kind to him, be honest with him, be where you say you're going to be, do what you say you will, do not be a people pleaser but say the truth, be supportive of him - don't take ABUSE from him but try to understand how absolutely devastated he is. And do be a good mother to your children and provide them with the examples you would like them to model themselves after in adulthood.
And do keep posting here, I know it's painful but everybody starts from some rung of the ladder and works their way up. You can do it too. You're not evil, you're just screwed up and you need to fix yourself. In a year, there will be change of some type....and hopefully progress that you help create. Be active in your life and make the change you want and be honest about it and be fair and compassionate to him.
Good luck!