I am going to refrain from being one telling you how you should feel. The anger and emotions are natural and even necessary to a point, but what everyone is trying to say -- albeit in ways we certainly don't agree upon -- is that they can consume you. I am confident that you do understand this, all too well.
I will diverge from some by saying that you do not have to relax your guard or pretend that the OP is (or ever will be) a positive influence on your children. To the contrary. To make such a pretense would be a disservice to your children.
But like it or not, she is (for now at least) being brought into their lives, and there is very little you or anyone can do about that. You have to come to terms with the fact that she is simply a part of the environment -- to which you must prepare your children. But the plain fact is, the world is full of sad, lost people who do deserve our pity -- but we should still keep them at arms length and in plain view at all times. You don't have to forgo civility or allow them to upset your inner peace, and you don't have to play nice-nice with them either, certainly not when they refuse to respect your own boundaries. It would be better to show your children that you are willing to act and do what's best for everyone's sake, even if that means establishing a sort-of peace -- while still maintaining and defending your personal and familial boundaries. (I can predict that some will disagree with the best approach to that.)
It is a fine balancing act -- and no, it is not and will not be easy to maintain.
