Interesting question. I think it's well intentioned but a little far-fetched.
To have my kids without my wife, to try and erase her from the equation makes light of God's providence, and the gift and beauty of our lives together, however painful the last 2 years. The woman I married wouldn't have taken the path my wide has now. People change. There are no guarantees.
I think a more legitimate and hard question is, "Would you have married her, realizing that not marrying her means you wouldn't have your children?" That's a much more honest question. It's a question about our lives and how we assess them. It's a tougher question about our own existence.
I would answer, "yes". Yes...I'd marry her again. Why? I would do many things differently. I would have loved her with a passion, clarity and purpose I lacked throughout most of my marriage. I view it as one of those "would you go back and change the past?" questions. Yes I would, romantic fool that I am. Deep down I probably believe my loss of nerve, my depression, my lack of emotional connection with her really sent her over the edge. I would have given us a beautiful life. She deserved to be loved better. The question arises, "Why can't you do that now, Theoden?" She's deeply changed. Let me be honest enough to say that, perhaps, my lack of love contributed to her rejecting our common faith. Now we have much less in common. We can't understand each other anymore. I am much like Theoden, I may have woken up, but some damage is, perhaps, irreversible.
Here are some other hard questions.
If you were guaranteed complete custody of the children, would you divorce your spouse?
Assuming you have grounds for divorce (adultery), why aren't you divorcing you spouse?
What changes must your formerly adulterous spouse make for you to want to stay in the marriage?
Have you been so hell-bent on keeping the marriage together and concerned over the welfare of the children that you haven't stopped to think, "What do I want?"
Fast forward 2 months, your spouse has a change of heart and ends the affair and recommits to your marriage. If, somehow, your marriage could be saved, and made workable, mediocre and somewhat fulfilling -- if not spectacular -- and your kids would have an unbroken home, would return to it if you felt that you could have a terrific relationship with someone else? Would you settle for a lack-luster marriage with your current spouse if you somehow knew there was a good shot at a great marriage with someone else? This situation, interestingly, puts us in the position of most WAS, except, we have "more" justification.
