Here is advice I posted for someone else. It fits your situation, too. It is just about the same as what Eli-Zor posted.
The first thing you have to do is to find out what is really going on.
I have very bad news for you: Your wife probably still is having an affair. Maybe with the same other man, maybe with a different one. Whoever it is that your wife is having the affair with, the affair is not over. Look for a prepaid phone. She wouldn't still be acting this way if she wasn't in contact. I have a very strong suspicion. At the very least, other man still is in her head. He may be contacting her.
Buy a few voice-activated recorders and some heavy-duty velcro. Put one under the seat of her car and in the house in places where she is likely to talk on the phone when you are not around or if she wants privacy. Keylog the computer if you can. Give it a week. I'm betting you will find out what's going on with your wife.
After the voice-activated recorders are in place, have a talk with your wife. Tell her that you love her and want to save the marriage. Tell her you are willing to work hard on improving yourself and improving your marriage.
Get your wife alone, no kids, no interruptions. Tell her that if she wants to save the marriage, she has 15 minutes to agree to meet your conditions or else you will file for divorce and she can pack up her stuff and go live with the other man. Here are the conditions:
1. She must handwrite a no contact letter to the other man stating how horribly ashamed she is of her behavior and how terrible she feels for risking losing you, her husband, who is the most important person in the world to her, and that if other man ever attempts to contact her again in any way shape or form, that she will file harassment charges against him. This is the content of the letter, nothing more, nothing less. It begins with other man's name, it ends, "signed" and her name. It contains no terms of endearment, no sorry it didn't work out, nothing else. She gives the letter to you for editing and mailing.
2. She gives you access to all communication devices and accounts, all passwords. She lets you know her whereabouts 24/7. She does not delete any emails, messages, texts, or calls from her devices or accounts - everything gets saved. If you find out anything has been deleted, you will assume the worst. There is no place for secrecy in a marriage. You have agreed to share your lives together. You can have privacy when you go to the bathroom, but there should be nothing phoned, messaged, or texted that your spouse shouldn't be able to see. Married people don't have things to hide from each other. Many if not most married people are NOT constantly checking up on each other, although they could. Would you care if your wife looked at your email or text messages? Would you care if she asked you where you were going or with whom? This is normal stuff EXCEPT for cheaters.
3. She blocks other man on facebook, deletes him from contacts, blocks his number on email, does everything possible to block him from her accounts.
4. She handwrites a letter of apology to you.
5. She gets tested for STDs and gives you the results.
6. If you want the details, she tells you the whole truth about the affair, when it started, how it started, and WHY it started, etc. Tell her to handwrite a timeline of the affair, starting with the first inappropriate contact, and ending with the last time she had contact with him. If the story doesn't make sense, she will take a polygraph to prove her truthfulness.
7. Your wife should destroy all of the clothing she wore when she hooked up with the other man. Shoes, dresses, lingerie, pocketbooks, jewelry, etc. It's a consequence of her cheating. When people know there will be negative consequences, they are less likely to repeat the action. It helps you to feel she truly is repentant and not just giving you lip service. It helps her to make amends to you in a material tangible way, which will make her feel better if she is truly sorry for what she did to you.
Tell your wife that you cannot control her. You can only control yourself and what you are willing and not willing to accept in a marriage, and how you react to her actions.
Cheaters are liars. They say anything to get what they want. Talk is cheap. Make her do these actions to show she really wants to save her marriage to you. Do not accept any verbal promises unless they are backed up by actions.
If she doesn't agree to these conditions, file for divorce. She really is not remorseful, not interested in committing to you, just interested in appeasing you with words. Divorce is a long process, if she later agrees to your conditions, you can postpone it to work on your marriage. If she is not willing to accept these conditions, which, if you really look at them, are not that much of a sacrifice on her part to save the marriage and which pale in comparison to what you will have to live with, then you are going to wind up getting divorced down the road anyway; might as well do it now and get it over with and save yourself weeks, months, or maybe even years of the pain of trying to negotiate with a lying cheater.
If she does agree, leave the voice-activated recorders and keylogger in place. This is to verify that the affair truly has ended. You should keep it up until you are comfortable in ending it, but monitor closely for at least two weeks.
Trust is important in marriage. Constantly monitoring is not healthy. However, in the initial few weeks after infidelity is discovered, it can be extremely healthy and helpful in restoring trust. You can cut down on the monitoring as you continue to discover nothing and your trust builds. Or you could catch her continuing the affair, which would save you a lot of time and trouble and heartache.
If it weren't for the kids, I would say just dump her, she is more trouble than she's worth.
If you think it would help, expose the affair to her and your families and friends. Tell them other man's name, that your wife admitted that she had an affair, and you have no way of knowing that the affair still is going on or not but that because your wife keeps deleting her messages with other man, you think it probably is. Ask for their support of your marriage and your family. Definitely do this if you find out the affair is ongoing.
I think the affair never ended, maybe took a short break, but they still are in contact, maybe even other man visits your area occasionally for sex. That's based on hundreds or thousands of stories on this website and my reading of your situation through your post. They were physical once, saw each other for sex, she's holding on to his love letters, this thing isn't just going to die an easy death.