He can only talk you round if you have a conversation with him - so don't.
First of all, spend some time really, really thinking of what it is you want. If you want out, then that's what you say to him.
Sit him down and say, "This is not working anymore and neither of us is happy. So it's over. Please leave". That really is all you need to say. If he starts ranting about how he wants money, tell him to grow up...he knows perfectly well you haven't got it.
I don't know how the land lies, but if you can kick him out, do so - and don't look back. Be fair about allowing access to DCs, but do not involve yourself in any conversations about anything else. It won't help, and you already know what he's going to say because he's said it before.
Once he's gone, get on to the Tax Credits people and start claiming in your name - he won't be entitled to them anymore, but you will. You should also be able to claim Income Support & money to cover your mortgage payments (think it just covers interest only, but don't quote me on that). Best bet is to get down to CAB as soon as possible for some solid financial advice.
You won't fall apart financially - probably you'll be better off, because the money he's earning and spending all on his deserving, little self
will be replaced with benefits to support you and your DCs.
Sorry, if this advice doesn't precisely fit your circumstances, I'm reading between the lines somewhat, but you are in a stronger position than you realise, so take control. And couldn't your well off mum (you lucky thing!) help you out a bit to get over the initial bump?