I think some men (not all) may be too concerned about appearing as if they are controlling or acting like a jerk. At this particular crossroads in your stitch, I think those two concerns may run secondary to you being strong in your boundary and firm with her on everything.
I don't think you should try to have small talk or sociable conversations with her. Not while she refuses to make any moves to quit her job or ending her online behavior. Not while she is lying and turning everything around to make you sound bad. Why? So she will not misconstrue your intentions or motives. So she will know this is not going to fly over in a few days and you'll be back to doing whatever she says. So she will see you are dead serious about it, and that she cannot use her usual manipulation in this case. The more you interact, the more susceptible you will be to her tactics.
You have a full plate at home, so as long as you are responding to the kids, I say not to add more stress to yourself by worrying what she thinks about you not having much to say.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!
