You're not hurting her by being this way, she is just temperature checking to see if she still has you on a leash, and placating you so you won't look out for your own interests (and the kids'). She knows that she has gone way out of line and overstepped her authority by taking the kids, and she knows you could go get them whenever you want to.
If you respond to any pleasant behavior like an eager puppy, she'll pull away again. She thinks she knows exactly who you are, what your limitations are, what you are able to and what you can't do, and how she can play you. Prove her wrong, it's the only way you have a chance to get her to reconsider anything. Right now, she does not care about your feelings, only about her own.
You are not supposed to detach from the kids. Call them as often as as much as you like. They should be with you at least 50% of the time, she's the one who left. She does not get to dictate your interaction with the kids.
"Questions:
1. Immediately stop all contacting throughout the day.- Do I not call to say good night to kids every night?"
Call them as much as you like, preferably get them home.
"2. Immediately withdraw his physical presence from her as much as possible.- My youngest Son is turning 2. I will need to have a small party or take them out to dinner or something. How to handle this?"
No need to include your WAW in this, I wouldn't. Get the kids and have a celebration with your friends and family.
"3. Do not recognize her birthday, Valentines, anniversary, mother's day, or any other holiday by giving her gifts.- What If she wasn’t cheating? Just ignore the day and don’t say a word period? No Card or acknowledgment? Nada?"
I wouldn't. Maybe a happy birthday - text.
"4. What if the mother is helping her financially to keep them at her house. MIL is like that. It's like nothings changed for wife except she is with Mom enabling her to eat cake. How do I approach this and breakdown walls by detaching/180/etc?"
You can't control this, but you need to discuss your own financial matters with an attorney.
M 16 yrs, WH62, P54 3 adult blended kids EA 11/13, BD1 6/14 PA fall 14, BD2 2/15 Piecing 2015, BD3 12/15 Separated 4/16 WH moved OW in 5/16 Divorced 6/15/17