I understand what OP is saying. I can't bear to think about being away from my children for weeks at a time, even with equal time on custody. And aside from how common divorce is, I know my family will be so different if we split. It is literally two families. I am old school and don't believe in divorce. It isn't "just as good". It has to be sometimes, but I think making it work is best. You can hate on it, but family values developed for a reason.Whether it is a sex worker or your ex, my points on your choices still stand. It doesn't matter who it is. To hold it as a secret is wrong and cheating.
You're stuck in old world thinking. If you have done nothing wrong with regards to the children, then there is no basis for any court to deny you access to them. It becomes a matter of who has custody for what lengths of period. Many men are getting custody as women are these days. Dual custody is a valid option, especially if you both can manage to live in the same school district. Many people who are divorcing are realizing that they may not have been good spouses, but they can still be good parents and co-parent without being married or living together. Keep this in mind with regards to your children. They can end up suffering more and learning the wrong relationship behaviors from you two remaining married. Do you really want them to grow up to think that a sexless marriage is a valid working one, and copy the kind of marriage you and your wife currently have?