Oh gosh, a few similarities here. My ExH slept with my best friend. We were in the process of separating (due to his other infidelities), but I hadn't left the home yet and she was pretending to be my friend, whilst sexting with him, which eventually led to them dtd.
My children were similar ages to yours (9 and 11). I never told them what happened, but they didn't go on to have a relationship, so your scenario differs - I think you will have to tell them, but try to stay calm when doing so (hard I know).
Regards Christmas, I would definitely take the kids to your parents. They can have Boxing Day afternoon with your Ex. I think you will fall in to a pattern of alternating each year. Same for New Years and other events. It can feel a bit crap at times.
The only positive side, is that if you meet someone new (which you will), you will enjoy some alone time with him. I realise that's hard to imagine right now. But, I actually met my DH only 2 months after I left ExH. Whilst I would love to always have had my children with me, I did enjoy certain times without them, just by making the most of it. For eg, when ExH would take kids on holiday, me and DH would have a romantic holiday just the two of us.
My ExH was quite controlling and the only way to get my own way with some things, was to get really fierce. He would know when he'd gone too far, and back down. I would suggest you do the same. Tell him that Christmas is not up for discussion. Tell him what will be happening, there's no room for negotiation. He lost the right to see them Christmas morning when he left the family. It was HIS choice to do this. Remind him, that when you start seeing a new man, it would be impossible for the 5 of you to all spend Christmas together. And I really would say that. Let it sink in, that future Christmases may well consist of his DD's spending the day with you and another man.
Good luck.