I'm going to tell you that I have an issue with the money. Keep in mind this is not telling you what to do, but my own opinion.
In your case she left of her own will and moved to where her basic necessities are provided for. Paying for her going out with her friends is not going to draw her closer. Welcome to being Plan B that still pays for her EA. My opinion would be to determine what is absolutely minimum needed to give to her for the sake of your children, and then the rest is up to her.
My thoughts would be to keep the house filled with groceries and continue to make car payment and insurance. I am thinking about disconnecting her cell and getting her a cheap pre-paid (flip phone without the browsers and apps that she uses to communicate with OM. When she needs gas, I can fill the car up. My only concern is that this will expedite the seperation or divorce process so she can get her court ordered $$. I make 6 figures so this would be significantly more than what she is getting/using now.
If a 180 is to encourage her to go after that job, then I would. KISS (Keep It Simple, Stupid) and validate. Not much more beyond that or you are pursuing. On the other hand, going out of your way to find other jobs for her is like fixing it AND enabling her. Let her experience the consequences of reaching beyond her skillset and doing things on her own. Point taken. I will not bring it up, offer suggestions and validate her when she does mention, or show empathy when she doesn't.
Goals I like these as a start. They are more centered on you and what you can control, which is??? Myself and my actions. I cannot control her.
180s 1. Very nice with good examples. 2. I will keep the house organized and clean. -Do this for yourself. I have not yet met a woman that likes a messy/dirty man. Drop the W reference. 3. Grats! Make your muscles hurt and rock that tank top! -Added benefit: Endorphin release. Love those things. 4. I will not pursue. -In your case, what does that specifically look like? My means of pursuit have just been simple things like asking her to come to church with me and children or go to activities that I do with kids on weekend. She always has an excuse so I'm not going to do it anymore. I have not asked her to work on our marriage or MC or really anything after the first few days.
You registered not too long ago and are just now beginning your first steps. Gotta get over the shock and clear your head before truly making headway (I beat my head against a wall for quite a while). These are a great start, and we'll keep adding them as you go. Focus on what is immediately achievable and build from there.