havent read all this but wanted to say - that i really dont think you can stay for the children - they will not thank you in the future.
My h had an affair - and we are still together - some of it is because of the children as it would have been easier for both of us without children involved.
Be have both worked hard on finding out why the affair happened ect and i have to believe he wont do it again (as does he of course).
I worried for a long time that he was only here for the children and i didnt want to live like that - i am worth more than that.
For me the turning point was when we were away together and i looked at my h and was overwhelmed with a sense that i wanted to share my life with him.
But i also know i could go it alone and there is a strength there i am not willing to give up. I will never again be so reliant on him for my emotional needs again. This makes me sometimes question whether this is complete love - and whether i am in it for the right reasons, but i do feel i love him - just in a slightly different (and in many ways better) way. I love him despite his faults.
My parents i feel stayed together for the sake of me and my brother. My dm is now ill and my dad is her carer. There is little love between them - she does not want to be cared for by him and equally he does not really want to care for her, but they are stuck now with no respect for how each other really feels. I vowed never to be in this situation as it is awful to watch.
Nothing is gaunteed in life but i owe it to myself to be happy with MY choices and not give that responsibility to anyone else (which is in a way what you are doing by saying you are staying BECAUSE of the children).
Talk to someone about how YOU feel and know that you can do whatever YOU want. If he chooses not to see the children then it is HIS choice and not yours and he will have to live with it not you.
Good luck and stay strong.