Oh gosh, I really do sympathise with you as I am in pretty much the exact same situation and trying to cope with the exact same feelings. The only difference is that my husband has never had the guts to admit that he had cheated on me/ is seeing someone else. Either way, the turmoil that you put yourself through (my main one is that I constantly feel that perhaps I was unreasonable in my expectations of him as a father and a husband and I drove him to do what he has done) is awful and, at times, unbearable. I have posted elsewhere on MN about the awful depths of despair that I can sink to and it was the brilliant advice of the other Mnetters that persuaded me that it wasn't all my fault and that things would get better eventually although there would still be a lot of crap to deal with.
Like you, I go through days when I think that if he were to walk through the door and say that he wanted to try again, I would welcome him back, no questions asked. Other days, I berate myself for being so stupid for falling in love with a selfish, immature, callous, coldhearted t**t who put his own interests in front of those of his wife and DS (who is just coming up to 2). Other days, I just simply loathe the man and feel sorry for him thinking that one day he will regret everything that he has casually thrown away and, having never had the courage to face up to it all, will never learn from his mistakes.
A lot of what I have done is on a practical level. I have found that having/ trying to have discussions about the whole situation with my husband impossible mainly because he stonewalls me/ turns nasty/ gets defensive ie. the behaviour of someone who feels incredibly guilty about their actions but doesn't have the guts to do something about it. As such, I have minimised contact with him and contact is primarily by email. There is no discussion about the emotive aspects of the situation, simply discussion about the practical aspects such as access, finances etc. That way, it is more difficult to get drawn into emotional conversations. Knowing that contact with him is on my terms and only deals with the necessities means that I can almost compartmentalise him and deal with him as I would a nasty chore at home. I'm not advocating this as a long-term solution but it does help whilst you are trying to rebuild your fragile confidence and self-worth. I know that, in the long term, I do need to be able to build up an amicable relationship with him but, again, it will be on my terms and at a time when I am a stronger person and able to cope with him.
I've also tried to start rebuilding my life without him. Since my DS was born I have made some amazing friends and, together with my school friends and other friends who were originally mutual friends of mine and my ex, I actually have quite a good social life! This has been really important as it can be the weekends and sometimes evenings when you can get really lonely and start to dwell on things a little bit too much.
I've also taken up a voluntary role with a local organisation and the feeling that I am able to make a worthwhile contribution to a good cause makes me feel better about myself (yes, there was a bit of a selfish motive there I'm afraid). I've also joined a gym which I've found great for getting rid of anger/ frustration etc.
Talking to friends and family has also been invaluable and is probably one of the best things you can do. If you are like me though and you don't want to always be a "burden" to friends and family, you can always post on here and there will always be a sympathetic ear/ words of advice.
I've also tried to stay on relatively good terms with the in-laws. As difficult as it might be, you may find them to be a good source of support and understanding. Certainly, I have had that from my in-laws although I was rather nervous about talking to them after it all first blew up. However, it was good to get their perspective on things and also an insight into where they thought things had gone wrong. I was surprised as they certainly didn't view their son as unimpeachable (I think that's the right word!
Your children will be a great source of comfort as well. As much as my DS frustrates me sometimes with his antics, it only takes one cuddle or little gesture from him and my heart melts all over again. I was practically in tears when I dropped him off at nursery today as he spontaneously turned round and gave me a kiss when I said goodbye!There will be so many precious moments that your husband is missing out on because of his actions. I know you say about your children growing up in a "proper" family but I am gradually starting to realise that my DS is doing absolutely fine without daddy always being around (answer to that was that he never was in reality there and when he was he wasn't that interested) and that they are hardy strong little creatures. It might be because DS is a bit younger than your DC but hopefully, as long as they know that they are still loved and that you and your husband will always act in their best interests regardless of the relationship between the two of you, then that will go a long way to helping them as well.
I have even signed up to internet dating the other day. I am not normally the type of person that would ever consider it but I have learnt over the past few months that taking myself out of my usual comfort zone can be a really positive experience. I'm not saying that I am already over my husband dumping me and my DS but, for me, it is just another way of slowly re-establishing myself as a person independent of my husband, rebuilding my confidence and having a little bit of fun along the way. I'm not expecting to meet Mr Right Second Time Lucky but it is a step to realising that there is life after this whole sorry mess.
The last bit of advice is that old tried and tested one of just taking one day at a time. That is what I am doing. Sometimes, I will have day upon day of crap and will end up posting on here feeling virtually suicidal but it just takes one good day to realise that it is all worthwhile and life will get better and that, gradually, all the horrible feelings and emotions that you are dealing with now will lessen as will the pain of what you have gone through over the past few months. By looking to the future and not dwelling the past, you will start to come through it.
I have just realised that this is an absolutely epic post but your message really struck a chord with me. I hope that some of my waffle helps and good luck! x