No matter how much you want to. You may feel like taking a hit out on the ex or running a front page article telling the world what an evil sob/bitch your ex is, but please don't. Blog it or diarize it secretly and securely or rant at your mother/sister/best friend/brother, but don't let it get back to your kids.
NEVER tell them how much you hate your ex, even if you wish them dead.
Your kids just do not want to hear it. End of story. They don't. Your divorce is not theirs. YOU are splitting with their other parent, not them. They love their other parent. Deal with it.
It's so hard to keep quiet about how your ex has done you wrong, believe me, I know (and I'm not saying I have a perfect score, either) but your feelings have nothing to do with your kids feelings for their parent and you have no right to try and change them.
I have never and will never allow my offspring to become alienated from their father. There have been occasions when, after an argument with the father, I have yelled "He's such an idiot!" or "He really does my head in", or words to that effect, but I have gone back to the offspring afterwards and reassured them that a) I was stinking mad when I said those things because daddy and I don't agree on this and that at the moment, b) that he's not actually an idiot, I just said that because I was stinking mad, c) that I shouldn't have said it and d) that daddy loves them tonnes and tonnes and no matter what happens between daddy and me, we will both always love them more than the universe.
It's been a hard slog for the other parent and me but we have a pretty wonderful relationship now as things go. The break up was bad for while - can they be anything but? - but throughout it all, he saw the offspring, spoke to the offspring every day, and with his wife we are a parenting team. We're not best buddies and never will be, not least because that's inappropriate, but our mutual offspring knows we are a unit and want what's best.