So so sorry you're going through this. What an awful betrayal. My advice is to work on what was drawing you apart. The good news (!) Is that it appears that the affair was more about attention, and the novelty and thrill of the sexual escapade and not emotional. Your wife is also remorseful. So 2 pluses in favour of you mending things.
So why did you both start taking each other for granted at a time when your children are less needy and more independent and presumably there is less pressure (in terms of time to have sex, time to spend together etc.)?
You mention you have your own business. Are you working all the time, even when at home? Do you have the energy to go occasionally out together as a couple after work, or is it the classic flop in front the tv? Did you regularly compliment each other, go away for dirty weekends? Buy gifts for each other? Go for walks together. As lovers, not just co-parents?
Sometimes we fall into a rut of thinking that because we feel we love someone its enough. But love is active and sometimes it requires structured planning to keep up esp. with children. I think we often feel it should just feel natural. But one piece of good advice I read in a book said 'treat your marriage as if it was an actual third person with needs, who will die if those needs aren't met' plan activities that will feed it and do them regardless of how you feel. So lets say you plan to go for a long walk/picnic together one day a week. On that day, you come home,and see wife had bad day. You're also shattered. But if you treat your marriage as a third person, you go becaus the marriage needs it, regardless of how upset, or tired you may be.
You can also plan in sex. Plan a long session, one day a week. Get rid of all distractions and plan to have fun. This sounds counter-intuitive, because you cant have sex to order, but once it becomes regular, it can become something you look forward to, and the body starts to anticipate it.
Essentially, if you want to regain a sense of security and faith in your marriage, you have to do things to rebuild it. You have to be proactice. You can do things everyday towards this. Its good to talk, and cry etc, but if you both wish to be together then half the battle is won. The question is identifiying where you've gone wrong, (what has your wife said?) and shoring up that weakness. Its likely by the sound of things she felt less attractive and loved (of course thats no excuse). I assume she has cut off this man and is working to regain your trust? You need to discuss concrete plans to fix the damage. If you work long hours, shorten them. Take drastic measures.
Best of luck
You can come through this and a marriage can be stronger afterwards.