Are you documenting the times he is w/the children? It's something you need to think about doing just in case you need to have proof of his MIAs w/the children.
Oh, your h was really pissed and I think it's because of all the party emails going back and forth. He's angry at himself and the world. Unfortunately, you are the nearest to him so you are getting the brunt of his anger. Why doesn't he contact the person who is sending out the email list himself? You are not his mother or his secretary. He is a grown man, is he not? Then I would tell him to contact the person himself and walk away. I could just smack your h for being such a snotty PIA.
I know it's difficult, but please try not to take his actions or his words personally. He's in a very hateful, dark place right now and you are being sorely tested and emotionally abused by him. When he gets that way, cut the conversations short, hang up the phone or walk away. You do not deserve this behavior and until you set some boundaries, he will continue to do this. Take back your self respect.
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.