I'm so sorry. I wish I had more advice, but I just wanted to tell you that only YOU will know where to go from here.
I can not speak from having this happen to me as a wife, but I can tell you that my father cheated on my mother for the entire time they were married (she finally divorced him in 1996 after 30+ years of marriage). I can speak from the viewpoint of the child in a situation like this, and I can tell you that I spent my life feeling like I had to protect my mother and her feelings. I'm 36 years old and I still feel like this. So it is something that not only affects you, but your children.
That said, IF you work it out and he stops this, then of course that is good for your kids. But if it keeps happening, your kids will take a lot of the brunt of it, too.
Also, I want to assure you that this problem is HIS not yours. There is nothing wrong with you that led him to this. Men that cheat often have very low self esteem and they are constantly looking for someone to stroke their egos. So unless he is therapy, he probably will do it again. You did NOT cause this. It is NOT YOUR FAULT.