Can't we all just get along?
This principle means that your job is to look at what you yourself can do differently to improve the situation. It is not to keep ruminating about what she, the other woman, should do differently.
Your assessment of what the other woman should do differently may have been perfectly correct. The problem is that you need to use your brain power to figure out how to fix your behavior, not hers. Focusing on what the other woman needs to change will just needlessly increase your levels of stress and upset.
So instead of wasting your energies on trying to get her to change, focus exclusively at what you yourself can do differently. Hopefully you then will be able to figure out how to deal with the tough situation more effectively.
3. Remind yourself that your job is to do what is best for the children. Fighting with the children's other mom creates needless tensions for the kids. Allowing them to have a positive relationship with both of you is what they need.
How can you get over a narcissistic obsession with how to isolate The Man from the other woman? That's the right question. Competing over who gets how much time, who is more lovable or to get back at your husband/ex for having or having had another woman in his life is totally out of bounds and will only sustain your distress.
The bottom line is that a mother and a stepmother have to share. Sharing time with the kids is a given. Sharing a connection with the same man, one of you as wife and the other as former wife and co-parent, is a given.