I’ll reply in more detail when I get the time, however just quickly…
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She's still lying to me even though we're separated.
This is something you’re going to have to work on.
Men get super caught up in right and wrong and blame being placed on the right place. Women get caught up in avoiding accountability and making everything they do someone else’s fault.
If you challenge her on lying about her plans on NYE, she will double down and things will ramp up badly.
You absolutely can not get involved with trying to hold a woman accountable for her lies when she’s in the middle of an affair. She will do anything and everything to avoid being at fault. This is normally when women start making false accusations of domestic violence/coercive control etc.
Do not engage. Tell her you’d love to have the kids on NYE and spend quality with your children.