You have to back off and detach from W, I know it is hard for you, but you have to.
The issue with the kids should have been discussed in the morning, not when she got home late. You should be thankful that she got home at midnight. My W stays with OM till 3-4am. I did the same thing and stayed awake when she got home, then argued with her about spending more time with DD and other stuff.
You must take all the power away from her re getting angry at her, questionning her etc etc it justify's her decision even more when you behave that way. And it makes you less attractive to her and pushes her towards OM.
Okay, so you did backslide, just regroup and start again. We have all done it so don't worry. It may take some time, but please detach from her. Then discuss things re kids when you are both calm.
AndyV M38 W36 D7 M 13 years Together 17 years W wants D mid Dec 06 (ring off) W wants separation early Jan 07 (she backdated to Oct 06) EA revealed end March 07 (Nov 06 W first meeting with OM) Hallmark moment "I care for you but am no longer in love with you."