Yes confront her. Tell her you know everything, give her all the details. Tell her you're going to contact her family and let them know what's going on and that you guys are splitting up.
Tell her that you aren't going to share her with another man and she is free to go. Tell her she should be with that guy if that's what she wants to do but you won't be disrespected in your own home, she needs to go to a friends house to conduct her relationship with the OM because you won't allow it to go on while you still live there in your own home. You will be civil with her when it comes to the kids (if you have kids) and she is free to go and do what she wants and you'll do the same for your life.
You can't chase someone who doesn't want to be with you.
Let her go, do your own thing, enjoy your life, you know about the affair, you aren't some dumb naive husband who thinks his wife couldn't be up to such things. You know better now.
