Fascinating that his family won't help him out. Is he a lazy, good for nothing wanker who has been sponging off you for a long time and, before that, from his family?
It's incredibly hard when you've been with one of these man children because it feels like you're abandoning them. They've spent your entire relationship convincing you that they simply are not able to do all these things that normal, functional adults do - work, cook, clean, look after children, plan activities, manage the mental load, shop, drive etc etc etc - and without realising it, you've slipped into feeling like his caretaker and, ultimately, responsible for him.
But remember this - he may think he can't do all these things because he's been happily letting you do them all (hopefully not my ENTIRE list, but I wouldn't be surprised). But of course he can. And if he can't, it's really not your problem.
However, be prepared - once he realises you're staying firm he will most likely swing between intense efforts to make you feel guilty and screaming accusations about what a terrible person you are. Most likely, he will also bring the DC into it and attempt to manipulate them and/or use them as a tool to manipulate you ("I can't fetch the children from school for you - why should I? You've just dumped me on my ass with nowhere to live).
You will, sadly, most likely have to move to get rid of him. Be prepared for him to disappear if you do - on you and the DC. Or, to use every trick int he book to stay with you - "I'll just come on the weekends" or whatever. He may also allow himself to be homeless and will send you messages/pictures of him living in his car, or in a park. Suicide threats are common.
It's really hard. If you're so inclined, can you pay a deposit for him somewhere - like lodging? Or help him look into what benefits he might be eligible for? Why doesn't he have any money?