Nesting after infidelity - is it even an option?

I am a 37M, my STBXW 39F. 14 years relationship, 8.5 years married with 2 girls under 4yo. DDay was almost a month ago - I discovered that she is having an affair with a married man. They appear to be "in love". She denied profusely, however I have hard evidence which I won't share with her for my own reasons.

I am pretty much after the rollercoaster. I realized that she is not my wife anymore, and I mostly do my best to focus on the future and how to be the best father under those circumstances.

In the first week after DDay while still in "investigation mode", i found that my WW brought her AP into our home while I was away. This happened at least twice that I know of.

For the past 3 weeks we did not talk about anything except out daughters, but today I told her I want to discuss the future and only the future.

She said she read about Nesting, where the children remain in their familiar home and the co-parents move in and out according to the agreed custody arrangements.

I obviously considered this option but I just can't see how I can live half of the time in the same house where my wife had sex with her boyfriend.

I am really trying to do the best for my kids, but it's just too big of a frog to swallow.

Am I being childish or egocentric?

Edit:

Given some of the comments, I will add a few details and clarifications:

  1. I filed for divorce 5 days after DDay. I thought I pointed that out in the original post but apparently I didn't.

  2. We don't live in the US, so anything you think you know about divorce involving infidelity is irrelevant. See #3.

  3. I consulted a lawyer the day before I filed. The main takeaways were: first take initiative and file, and second - it doesn't matter wether I have proof or not. It just doesn't.

  4. I will not ask her to move out nor will I leave. None of both is at the beat interest of my daughters at the moment.

  5. Anything involving informing her family, my family, AP's wife, or whomever is just not in my best interest right now. I need her to be as cooperative as possible until we have legal agreement. Yes I confide with my closest family and friends, but this has nothing to do with her.

  6. No, I do not believe a word she is telling me.