Re: My wife is at a crossroads, I could use an outside perspective.
So, what has your wife done to ensure that the reconciliation is going in the right direction? Is she now transparent with her email, phone and social media? Does she tell you where she is going, i.e. account for her time when you two are apart. Most importantly, is she no longer in contact with the other man? Are you verifying that no contact is being enforced by her?
Was this a physical affair or purely emotional? If you caught the 2 of them together, I'm assuming it went physical? You bear no responsibility for her cheating on you. That is 100% her. You two share the problems in the marriage up until the time she decided to engage in an EA/PA.
I know you two want to be great parents, but at the end of the day the two of you need to see each others as lovers first, not as mother/father of my children. If the reconciliation is going well, I hope the two of you learned this. You cannot let your kids get in the way of your marriage. Easier said than done, but you have to figure out a way.