For me, a big obstacle to detaching was/is fear of the unknown, and fear of the consequences of separation/divorce.
In my case, actively seeking out info about how a divorce would work from an impartial lawyer, and sketching out what I would do if things headed in that direction... those helped me fear the unknown less.
I also gave some serious thought to what my life would look like without WW in it, and what were the positives that could come from that scenario. Things like getting away from the toxicity, not worrying about whether me using the "wrong" hangers for clothes would cause a blowup, spending more time with friends, eventually finding a new relationship with someone who appreciated the good things about me rather than just harping on the bad.
As I mentally took those concepts for a test drive, I started to believe a bit more about my current situation what we ultimately relearn with every crisis we encounter in life - that we'll be ok. We can even thrive if we approach it with the right mindset.
For me, I had been unhappy for years, but now I'm working through a lot of the habits I had that just weren't working for me and have grown a lot. I'm ready for a much better relationship that what I had with my WW. I'm still hopeful that that new relationship can be with her, but if it's not I'll still be ok.
Kids are a variable I don't have to worry about, and I can only imagine how frustrating it is, but if the scale of your personal catharsis and transformation has been anything like mine, perhaps you can look at it as the kids will be better off with the new you - even if it's only half the time - then they were with the old you? I don't mean that in a disparaging way, I just know that for me personally the "old me" wasn't of much benefit to anyone because of my funk.
Me, WW - Upper 30s BD - Apr 1 2016 EA - Apr 7 2016 (discovered; ongoing for months; did not confront right away) Confronted wife about EA - May 17 Wife sent NC email to OM - July 11