I've been recycled willingly multiple times and it often came when I was doing well with my life without her. In your case you're doing what's right by your kids, and have found someone else. She cant have this. In her sick mind, you belong to her ... .for life. The thought of you moving on with your life with a new woman is unbeatable. Don't buy it.
Ask yourself what has she done to change? If the answer is nothing, well do yourself a favor and stay away. Believe their actions not they're words.
No you're right. She hasn't really changed in actions. Her anxiety only started when she learned I had a new woman in my life. I guess I don't know how to give her a chance to prove herself to the kids but with the understanding that I am not part of the package.