You are completely inconsistent. She tries to screw you over and you ask her out to lunch? You really just look more like a doormat who only reacts to her actions instead of getting some self respect and keeping boundaries for yourself.
This kind of action will only bring you farther away from your goal and stuck wherever your W wants you at that moment.
Also, I do think the inconcsistency is what is the main thing that is hard on your children. They are probably so confused as to what is going on with you two.
Time to make some boundaires and stick to them and display some more consistency rather than reacting your wife's moves.