I think its good to try to foster a relationship between the kids and the ex, but if their a bit older or its really a bad situation than I wouldnt push it either.
I have said the same things about my ex manipulating me and making me take the blame for everything. I've vented to my bf quite a bit. He's been a good sounding board and helps me get my head back on track.
He'll say "and youre letting him bother you because?" He'll also tell me every so often that I'm being stupid for letting all that crap get to me, and you know...I have to agree.
I know its hard, but you know that these are really ex's issues..not yours. If they want to lash out because theyre irritated, than thats their problem, and we need to learn to blow it off. Otherwise what we are doing is ALLOWING them to upset us and make us miserable.
Why give them that power over us? You know youre in the right. If he doesnt see that, than tough.
If I remember right, your kids are teens. I think they are old enough to decide how much of a relationship they want with their dad now. My girls are older, both in their 20s, but neither will talk to their dad now. It's something that will take time. A friend of mine gave me a good analogy. If you have a deep wound like a cut or a twisted ankle, you are told to stay off if it and let it heal. If you put pressure on it too soon, it won't heal correctly. She told me the hurt of my girls was like this. They need time to heal from the fact that their dad has become an adulterous liar. That he left their mom for someone else. Your kids need to heal from their dad walking out on all of you. Don't pressure them. Let them heal. Then let them decide when and how much of a relationship they want.