Your kids will be happier and better taken care of if you don't have to extend the energy to placate a spiteful narc. It might take some time for them to realise just how much their dad is playing with their emotions, but they will see it eventually. Better for you to get some space to be able to shore up your defenses to be there for your kids.
I wish my mum would have been honest with me about how awful my dad treated her during their divorce, but she was trying to be neutral for our sakes while my dad used everything he had on her to convince us he was not to blame. As an adult I have a much wider view on the whole situation and can see both of their roles in the failure of the relationdship, but back then (I was 13 for frame of reference) I would have wished for her to be honest with me so I wouldn't have felt so lost with what my dad was doing to me too.
Emotional manipulation, hot- cold, one day a thing was ok, the next it was the worst thing I ever did, buying us kids with money, threatening us with reducing my mums alimony if we didn't do as he said, claming I was too fat, too arrogant, too stupid, too smart for my own good, etc. All not to lose control.
So while it is not a bad thing wanting to stay neutral, especially when you have an ex that works with you on that and wants to keep your kids happy too, for your ex they're not people, they're tools in the toolbox to make you hurt because it's one thing he knows you care about a lot.