You are, understandably, looking at this from your point of view. But they, understandably, are looking at it from theirs. It seems clear from your post that you ended the marriage and he did not want it to end. Given this, it is hardly surprising that he has headed straight for a woman who has already expressed interest in him. This actually makes sense from his point of view. You are clearly in the ' I don't want you but I don't want you to move on yet', stage. Which is understandable. But from his perspective, moving on in part of his healing from the unwanted end of his marriage.
From her perspective, her husband died. Grief can do weird things to people, they handle it in different ways. None of us know what was in her head when she was flirting with your husband whilst you were married. It may have been harmless, a desire to still feel attractive or alive, or that she could still flirt. It might have been more than that. But nothing happened. Once he was free, well, to be blunt, she's widowed and lonely and saw this as a chance of happiness and to start a new relationship and move on with her life. And he's single and you didn't want him.
They are living their lives from their perspective. And they are both single. None of what they are doing is to hurt you. Its to heal both their lives and move forward from a brokenness that neither of them wanted.
He is a dick, however, for telling your children. That's completely self-absorbed and shows an absence of an ability to see things from another's point of view. I can see why you ended the marriage if that was typical behaviour. 
I also agree with PP that none of this is a feminist issue.