Drew is right. It's not about you. That makes it no less difficult to accept.
The thing is, you need to accept it. Start with that. Acceptance. I mean really work on that part. Because once you accept that although it was sudden (it was) and unexpected, it did happen. You need to accept it much like you would a car accident. You didn't plan it. You didn't want it. You didn't cause it. But it happened. The how and why become much less to deal with after that.
For what it's worth, I have met many people on both sides of the coin, Tad. The faces are different, but the stories are similar. The bible is full of similar stories. It's an old story among humans. It happens. It happens because we are human beings. No other reason really. It can be sad, especially because of what happens to the family (i.e. kids, friends, etc) that supposedly have nothing to do with it.
Your kids are telling you what they saw and what they are going to believe. The saddest part of it all is that they have to live with their mother's actions and have absolutely no say in what she did to them. You have the option of realizing she isn't family. You lost a friend and wife, but they lost their mother for however long that lasts for them. You can get another wife/friend/etc. They can't get another mother that gave birth to them and is the rock of their family.
They luckily have you to show them how to go on. How to accept what is, vs what should be. Time to focus on that and your mother's health and yourself and other people that want to be in your life. Time to accept what is.
Your ex will live her life and figure herself out with any luck. She may not. Either way, you need to accept what happened and accept that she is not able to be part of your life. At some point, you may decide you don't want her to be part of your life. But that starts with that acceptance (see the pattern?)
Peace, AJ
"Our lives begin to end the day we become silent about things that matter" MLK Put the glass down... "Yesterday I was clever so I wanted to change the world Today I am wise, so I am changing myself."