Hi OP
It's not clear in your OP but it seems you've got him to leave and live elsewhere, that's good.
Hold your nerve now. What's made you post this, at this time, about whether you should give him time/another chance?
Perhaps it's because you've had a more peaceful time and you feel your head is clearer to think. You feel you can see a difference. Emotionally, you so want this to be the sign he's changed and it might work. All this energy and thinking time from you.
He's in your head because he hurt you over and over again. This is a trauma bond and is worth googling and reading up on.
Same for "sunken costs fallacy".
You must stay seperated from him. You have tried to help him, offered him love, family and a stable life for a decade.
He's chosen to stay in his own preferred behaviours, he's allowed nothing to get in the way of his various addictions. He is in active addiction. Any real change in his life will take YEARS of consistent work and therapy. From what you've said he isn't even at the start of such a process.
He may never be.
I know you want your love to fix this; you want the good parts of him and of your relationship to be enough for him to live a real life. Step away. You cannot fix this.
There's so much trauma in your post for you and the DC. Protect them. Protect their Mum whom they depend on entirely.
There are psychological reasons your ex makes these choices. And that's for him to figure out if he ever wants to.
Make no mistake though, he is CHOOSING to abuse you and the DC. You can choose to leave all of it behind.
You don't need a relationship in which lie detector tests feature or are even thought of.
There are equally psychological reasons why you have stayed with him - you've been caring, fixing, the strong one, maintaining hope. Please find some therapy. Start with reading. You probably don't have tons of time w 3 DC but snippets of good quality info online will give you some insights to build upon.
He is so dangerous. He is unthinking, acting on impulses and addiction. He will not be able to modify his behaviour.
He uses Class A drugs in the home of his children. He repeatedly pays for sex. He has " gone through with it".
He went for a lie detector test and manipulated the questions, then said he'd admitted to more than he'd done to try and make you trust him. It's chaos, it's destructive and you can stop it.
He has already put his hands around your neck. This is very very serious. He could have killed you right then and there. This isn't fixable.
What do you think you deserve and what lifestyle will mean you have a happy life?
It's not this.
What (resident) Dad and lifestyle do you choose for your beloved DC?
It's not this.
You sound strong, maybe stronger than you think. You're right to be disgusted. You're absolutely right not to trust him.
Put your DC and yourself first. Team of 4.
Get STD tested. If you can move, consider it. If not, make some changes to your environment, make it even more yours and DC safe space.
You'll have wobbly days, maybe that's why you've posted. Accept them, it doesn't mean you've made a wrong decision. You being seperated is right 100%.
He could have killed you. He will be violent again and next time you might die. Your DC would be motherless.
He cannot be allowed to pickup the children in a scenario where you suspect he's using cocaine.
He's controlled you and your life with his abuse for long enough.
End the trauma by seeing it and disengaging from him. You're already doing so well.
Get legal advice.
Ask for help and support.
https://www.womensaid.org.uk/
https://ukna.org/
https://domesticabusecommissioner.uk/
https://www.saferplaces.co.uk/news/are-you-in-a-trauma-bond
https://www.psychologytoday.com/gb/blog/love-lies-and-conflict/202001/8-reasons-women-stay-in-abusive-relationships/amp