So guess that leads to my question, how do you establish a connection with a WAW? She has said that she's given up finding a reason to try again. So what's the next step......
You work on YOU. Maybe your W comes back or maybe not. You cannot control that - and yeah, that sux. It is a fact though.
So, you have a couple of choices. First, you can give up. Second, you can continue to work on improving you and your R with your kids. Making yourself a better person = making you more attractive to your W. But remember, the work is for you, not her.
She will notice your work. What she chooses to do about it is HER decision. You just make yourself available for her to see those changes.