Please, please, please @Cryingatthegym ignore these messages. Do not engage, he is ruthlessly pulling your strings.
Yes, it is honestly, literally unbelievable the distorting lengths they will go to to attract and keep your attention, to knock you off course and make you doubt yourself.
And his messages, his behaviours, his 'comforting' of you are all designed to feed your addiction to him and the rollercoaster, emotional and otherwise, of life with him. And, like any other drug dealer, he has no principles or morality when it comes to the impact he is having on you (and your children).
I get it, believe me I do. But the only way to break the addiction (trauma bond) cycle is to refuse to engage in it; you need to clearly see it for what it is. As others have said, what matters here is your children; you cannot allow the dynamic between you and this man to affect them any more. That is why people are talking about the 'grey rock' strategy - because it removes the dynamic; you can interact with him, but it is minimal and comes with no emotional energy or investment from you.
And it might not be my place to say this, but please don't tell him any more about you and him being 'finished' because otherwise you'll lose your daughter. This simply gives him more ammunition - basically, you're sharing with him your deepest fears and (if he's anything like my ex, and I sense he is from how you describe him), to be blunt he doesn't give a fuck - he's prepared to do things that puts your daughter's wellbeing at risk, you know that. So, don't share anything with him, because he'll use it against you, and you'll break yourself again and again against that despair of wanting him to care about you.
Oh, and don't beat yourself up about the sex, it happens, but please don't wait till he moves out to start on the 'cold turkey'. He needs to look in your eyes and know that you 100% mean it - otherwise you'll find yourself in the cycle all over again. The cold turkey starts right now; it has to. However appalling his behaviour or outrageous his claims, they are nothing to you.
You've got this, and we've got you; as someone says, let this thread be your comfort - draw energy, understanding and resilience from us.
(Sorry to be so direct here; I stayed (or let him stay) for years longer than he should have, because I kept getting drawn back into the vortex of thinking he might change / care / be 'himself' - and guess what, it got worse and worse and worse. For your sake and the sake of your children, reduce your expectations of him to zero and focus on your future, which I promise you will be a million times freer than where you are now.)