Do not even consider the "other" as a challenge. Wipe that thought out. It will hold you back - do not let your Psyche use it as an excuse. It is not about weakness.
You talk about respect. Respect yourself and your children as well as him. You do not love him now as you once did. Make sure that you grieve that fact and that you have both reached, and accepted a more realistic attitude to love. He is not the same person that you once loved. He has betrayed your trust - and your intimacy level will never be the same. Do not use Lust and memories as your weapons against "her". She is not really important in your life - in a strange sort of way. The girl that you are that first learned to ride a bike and so on ... had her first period ...
It is probably hard to find a sexually loyal mate these days even if you are living in the same house. I am not sure that the title "marriage" means much to most men really given any seductive opportunities - mental or real - where they may not to be discovered.
Distance is hard for men, and women, that is true. You must have both known that at some level too.
Your quality of family life should be considered also. How interested is he in the children? How much is he there for them? Could another man give you the love and support that you want? How old are you? Are you still attractive? Go to the gym if you are worried about your weight and have any relatives to look after the children. It is a heel when we have to look after children and cannot excercise after childbirth.
If you do not feel good about the answers to these questions ... ?
He has changed in your eyes. DO NOT CHANGE also in your OWN eyes. That is something that you will not recover from!! Do not go down to his level certainly - as I can see that you have not. There has been no talk of revenge or one-night stands. That makes you a very special person. Do not forget that.
Also - do not expect that over time he will continue to accept your belittling of him for all of this! Though wholly deserved. Over time you might become the irritable "shrew" and there will come the day when he will turn around and say that he has paid his price!! And the children will not understand. He will then take no more - he may even be already humouring you. I do not like the fact that he was not fully honest at the beginning. You know that you would have been. And then he did it again because he thought you were both over!!!!!!
You certainly must go to Relate so that you can see what his eyes look like when he is questioned by another Party. There you see the truth. It is in the EYES - what you see now - and also what you see with the third party beholder. Watch his expressions. There you see whether there is real grief or not. And whether you will be a wreck years down the line from this. Or a happy family doing Christmas.
I hope you make it work. But I hope also that you preserve yourself. They will go together only if they are both really true.