So, firstly apologies for just jumping into your thread OP. I have, however, read all of the first thread and this one.
I am you ten years down the line.
I was married for over twenty years, with three children, and my ex left me for OW. I totally get and went through what you are going through those first months. I too couldn't sleep, barely ate, but held it together for my 3 teenage kids.
We were all devastated.
So, what I want to point out:
You are stronger than you think. If somebody had told me that I would have coped, a year before the bombshell, then I would have doubted them. But, I did. Initially, it was a minute by minute. Then hour by hour. I barely ate, I hardly slept. I went from sick gut wrenching anxiety, to anger, to sadness, to shaking and sobbing and then back again on a loop.
Everyone said, "Soph, you're amazing, you're so strong" and I, inwardly, thought, hell you don't have any idea. But the thing is, I was strong, looking back, because I had no choice. I had three kids to put first and I did. You too are strong.
So, fast forward. 10 years on. He is still with OW. Not happy. Has regrets. Tough.
The kids: All adults - in their mid twenties: 1 has contact with him and sees him occasionally. 1 sees him less - perhaps 4 times a year. Youngest - DS - who was 13 when he left - never sees him. He too, calls him by his name and never 'dad'.
What helped me: Filing for divorce and pushing this - gave me focus, made me angry (and angry helps, believe me). Getting the best lawyer money could buy - I can't emphasise this enough. I got in debt through doing this, but the settlement she got me was worth it, ten fold.
Don't underestimate the effect on the kids. Adult, teenage ... irrelevant, they will, in their own time show signs of being affected by this. I never, ever, bad mouthed their twat of a father in front of them. But they work this out for themselves. They make their own choices. But here's the thing: your ex will blame you for twisting their minds. Ignore this. Do not respond to this at all. My ex said the reason our DS didn't want anything to do with him was me. Of course he did - typical projection. Ex couldn't face the reality of what he had done, so he blamed me. The reason our DS washed his hands of him, was because he felt abandoned, ignored, and his mum was left holding it all together. But the reality was too much to bear - so easier for Ex to blame me. You will get this - I guarantee it - ignore it.
Ultimately, in hindsight, I want to say that anger is better than "what ifs", you will get out the other side. You will get to the place I am at now, which is, that at least these two wasters ended up together, so two decent people didn't end up being hurt by them.
In your previous thread, you alluded a lot to Romeo and Juliet, like it was the ultimate love story "us against the world". Well, OP, I teach Romeo and Juliet, and it never works out for the main characters. It's tragic. For the two main players.
You are not one of them though - you can, if you detach, focus on the here and now, and not past, walk away to your happy ending.
I did.
I wish you well 