Victims of Psychopaths Community Group
Is he or she a sociopath or psychopath? Think we're only talking about serial killers here? Psychopaths, sociopaths and even narcissists come in every walk of life, every career level, and every socio-economic category.

I hope you have a strong network of support. Emotionally, spiritually, legally, whatever it takes to keep you strong and safe. I hope to be able to provide you support here. xoxoxo
Winning
Control
he loves to get a rise and emotions out of you. When he does he can manipulate and control you. This makes him feel better about himself (and likely relieves his boredom) likely he wouldn't want the children anyway - as they don't fare too well with responsibility.
This whole cycle of
When he is weak threatening to take your children
When he is strong - wants you back
Is indicative of his own level of low self esteem. Likely when he feels strong and wants to get back with you he likely thinks it will work. When he is threatening to take the children - he is merely weilding control over you.
Best you can do in parental situations is to treat it as a business transaction with no emotion so that you cant be manipulated. I also wonder though - if it is constantly changing - are you constantly changing your mind whether you want to be with him?
This is quite a toxic situation that will affect your children. Its the push and pull. Which could go on forever. The best you can do is to put the needs of your children first. And do what is right for them. Within the law.
No he will never move on - as you have his children - and he sees his children as an extension of him (like his arms or his legs) they are HIS he thinks.... so therefore he sees it that he therefore also owns part of you.
Sociopaths always have narcissistic rage when losing control - so that is why he probably threatens to take the children - as I expect that time you are being cold and indifferent towards him and he is looking for an emotional reaction.