Fmly1st, it's hard with kids because you can't completely cut off contact with your spouse and you want to keep them as comfortable as possible by making everything seem normal for them. It might take some practice finding the right balance between NC and communicating about the kids
I have experience now with my husband having several affairs. One thing about affairs is that they end after awhile in most cases (like almost all I believe?). There's not much you can do while your spouse is having an affair to make them end it but you can do the right thing to make your spouse see returning to you as the best option. It seems you have a lot of good clear advice from this thread to follow. It's still overwhelming but if you develop confidence that your marriage can be fixed and you believe in the process that needs to take place then it will be get easier.
I saw a counselor when my husband left the first time who said "I've seen this many times. He'll be back in about eight weeks. Don't worry." At that point I gained confidence and I also followed the DB book and he came back. Coming back or ending an affair isn't the same thing as fixing or saving a marriage though. Once they come back the problem isn't yet solved, so it's a long road. You love your wife, and your wife has her reputation with her family and your children at risk. Perhaps she's even thinking of divorcing you and starting over with this other man but she hasn't actually done that yet. She'll definitely have a reality check when she starts that process.