Do lots of research on narcs and trauma bonding. The hot/cold confusion is exactly the unstable emotional state he needs you in to be vulnerable.
But whilst you vacillate in his dramas - all of your finite time, headspace, emotional focus and physical energy is directed to him - you have not then got enough for your DCs.
You cannot be in two emotional places at once.
Your DCs need YOUR emotional presence and availability - they only have one functional parent.
Their family has broken down and they need extra focus from you to support their emotional development after this devastation. They don’t need you drawn and consumed negatively by your xH. So do what you can to detach from him, emotionally protect yourself and turn towards your DC.
This is v tough. You have all been v damaged by him. He still has emotional power - but you can change the dynamic and reverse out of this. You may need some professional support to help you through. Also get everything out in the open - tell people the bad things he did - make it real.
As others have said - minimal communication:
Email only re DCs. Tell him you will read them once a week on x day and reply on y day. The email account will be reviewed by a friend to filter any nastiness. Block him on everything else. Set up a new email account.
Give him zero info about you life or insight into your feelings because this is fuel and any nugget he will look to exploit. Vanilla, non committal, emotionless, vague responses if you have to dialogue - and also have an exit strategy “I am going now. / Sorry can’t speak. / I am busy” etc.
The detachment is to stop triggering the toxic bond - to stop him yanking your emotional chain.
Relish the emotional freedom that he is not in your life this minute, hour, day and scrub him from your mind because that takes away a positive, happy emotionally attuned and engaged Mummy from your DCs and leaves them with a distracted, sad, hurt preoccupied one - and they will sense and absorb all of that themselves.
You all deserve better.....and you can have it. Just takes a strategic approach, clear goal and support along the way.