Re: Asking for honest opinions on this apology letter to my wife.
I think the first part of the letter is pretty good, but you don't say HOW you are going to change. No offence, but "prayer" does not change your bad habits. Getting therapy with a psychologist who can help you identify your issues and then work to fix them is what lasting and meaningful change requires. You did a lot of things to damage your marriage. Typically people don't do these these to purposefully be desctrucive. They have deep-seated issues that need time to untangle and heal. It's great if you want religion in your life, but that's not the only thing you need to do to become a fully actualized person.
Your word does not hold much value right now, unfortunately, because you cheated, which required you to lie repeatedly. Talk is cheap and what counts are ACTIONS. So instead of your last paragraph, how about something like:
"I am so sorry that I was never able to show you all the love and admiration I have for you. I am so sorry I chose to deal with my life and my unhappiness in myself through unhealthy and destructive coping mechanisms (cheating). You should know that you were never the problem and it was never your fault. It was my own insecurity and weakness that has caused this mess.
I am beginning to work with a counselor to work on myself and all of my issues that caused me to act out and hurt you so badly. I know it is probably too late for us, but I did want you to know how truly sorry I am for hurting you. I love you deeply and I am devestated that my efforts to change may have come too late for us. Nevertheless, I am committed to becoming a better man, a man who can give his wife the type of love, trust, and commitment that she deserves. I still want to spend the rest of my life with you, but as the man you deserve, not the man I was. But I know my words don't mean much right now because of all of the things I've done and you are wise not to put your faith in my words right now. But I hope in time you will see that I have changed, through my actions.
I am giving you the space asked me to give you and will be working hard on myself going forward. I will understand if you have no desire to wait for me, but please know that I will always want to hear from you and that I will always love and respect you."
Then you have to do what you say you are going to do. Don't call her, just work on yourself. Maybe in a month or two you can call her to check in. Or maybe she will call you.
There is a good chance that she thinks this is just your lame attempt to get her back and that you won't actually follow through with working on yourself. This is your chance to prove her wrong.