You are getting good advice here. Your H is simply justifying his actions. Think of it this way, if he really believed in what he was doing would he have to justify it to you? Or anyone else for that matter. When you were dating him did he go around justifying why he was dating you? I don't think so. The reason he is doing it is because he is still convincing himself. He knows how wrong it is, he sees how it is hurting his family, he knows the lack of chacater it is displaying. If you step back and use the addiction analogy you can see similarities.
An alcoholic will justify that next drink in any way they can. It's just one, I'm not addicted, I can stop when ever I want, If it was more pleasant at home, I wouldn't need to drink, and on and on. Same concept with your H. His words are simply HIS justification to make what is going on in his head easier for HIM to accept. They have very little to do with you, the kids or anyone else. If you can use this analogy to lessen the sting on his words it really helps. You know the truth of your R with him. You portray your truths and let him justify his. I bet I know who will come out the winner in the end!!
PDT's suggestions if keeping things factual is excellent. It is very hard to discount fact. To take things further, set up a schedule between you and H with the kids. Something that is written and agreed to. As much as it hurts to have OW around your children, their father will always be a part of their lives and every child should have both parents involved intheir lives. There are exceptions where warranted, but I have heard nothing from you that would suggest any of those exceptions are present. I believe a schedule will allow you some relaxation time and give him a sense for what life will be like as a D'd parent. It isn't easy.
Bottom line, try not to let his inabilities become your liabilities. Stay firm and confident. Be positive and supportive. Let your character shine through and you will never have to hang your head.
