If I'm completely honest, I have never forgiven my father for the lies and deceit that happened before my parents marriage broke up. I understand/understood that marriages fail even my parents. But why couldn't he have left my mum then started seeing other women?
I naively believed that my father wasn't the sort to lie to his whole family (not just my mum, but us, his parents & sister etc) and I do see him differently now. I can't help it - he put the excitement of an affair before any thought of his family.
My mum is now much happier without him though it was a very very painful break up for them. No happy ending for him - he lurched from one needy adoring woman who made him feel "in love" for a short while to another and now lives in a caravan trying to persuade anyone who will listen about how sorry he is and how he still loves my mum (I don't actually believe him btw its just a pitch for sympathy).
It would be much more beneficial for your whole family (including your own self respect) to either try to make your marriage work without OM in the picture or to be honest with your husband and children and leave.
I am not without experience or understanding - I once had an affair with what was probably the love of my life who was married (I wasn't). I found it impossible to resist because I truly loved him - so I broke it off over the phone. I told him what I would say to you - "either try and make your marriage work (which means giving me up) or be honest with your wife and leave. If you leave we can then try making our relationship work"
He chose to stay which hurt like buggery and I have never married. I still think it was the right and honest thing to do and I genuinely feel he made the right decision.
If that is smug or taking the moral high ground or whatever, so be it.