I feel really bad. I'm with my ex-wife whom I was married to for over ten years. I went out with some buddies and got drunk. I made a mistake and cheated on her with a one-night stand. Does the Bible say tell the Lord and repent or does it say I have to tell my spouse? I know my spouse and I are living in sin because we're not married anymore. This thing will never happen again. If I tell her it will kill her and the kids. Should I keep this between me and God?
I find it puzzling that someone who is living a sinful life suddenly is worried about the fact that he added yet another sin. You are in the midst of sexual sin and you sinned yet again -- the only difference is that you did it with yet another woman whom you are not married to. You got drunk, which is also a sin. You need to look at yourself seriously because such a life will not get you to heaven. "Do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived. Neither fornicators, nor idolaters, nor adulterers, nor homosexuals, nor sodomites, nor thieves, nor covetous, nor drunkards, nor revilers, nor extortioners will inherit the kingdom of God" (I Corinthians 6:9-10).
What you need to do is straighten out your life and get right with God. What you need to apologize to your ex-wife for is not remaining married to her and not marrying her again before moving back in. You need to apologize for not living righteously. There is no requirement that you need to detail all your sins. What is required is changing (II Corinthians 7:10-11). Get married. Stop the drinking. Go to God and humbly ask for forgiveness for all your sins and start living a life worthy of one called a child of God (I John 1:9).