How to end this mess?

[Adhom]

You compounded your terrible luck with some terrible choices and now this is what you've got.

[historyfan]

Which mess? You acted in selfish manner.
Your wife and children are in extreme pain. You seem oblivious acting without any empathy.
They need grief counseling--yesterday. And you need it also-- along with some for finding out why you are narcissistic.

[Anabasis X]

IM sorry for your loss, this must be really difficult for you and your wife. If I were to give any advice, the first step would for you to take full responsibility for you stepping out on your marriage. Id advice a lot of counseling, independent and as a marriage. Even if you two decide to work it out, it will likely take you years to repair what your infidelity has caused. Yikes man.