She has her cake, she's also eating it. You've basically just added some icing and a cherry to it by considering giving her time because she's 'confused'. She has a husband and children, and is *completely* disregarding your relationship with her, and her responsibilities to her children. *You need to remember the responsibility you have to your children*. They are number one now, no questions asked. At the moment you're teaching them it's okay for your wife to not respect you, that you have no respect for yourself. And lemme tell you she's not respecting you at all. AT ALL. She's being *incredibly* selfish to the detriment of your family. 

She's not confused, she's only erring because you provide her a nice place to live. If you let her, she'd be over at this guy's house multiple days of the week and spending your earned money on lingerie. People who love people, don't fuck over that person they love by cheating and not considering their feelings or the impact it will have on them. She lied to you for two months. Like honestly, dude. 

And really, even if you waited around and she picked you in the end, are you *really* going to be able to trust she won't do this again? She won't cheat? Because you not doing anything is basically telling her that you're a doormat. 

She's not ending it with him, because you're not ending it with her. She's sitting pretty right now. Get yourself a lawyer and get your head out of the clouds.