Will you be eligible for the council housing if your arrangement becomes known? How are you going to explain a bed big enough for two and the lack of any sort of divorce if your status is questioned? Are you claiming all the benefits you could if you were divorced?
That's not really the main issue here. The main issue is that he is completely tied to his mother and feels he can just walk away from his real responsibilities.
This man has stolen money from his wife and children and given it to his mother, has stood by and seen his family lose their home and all they own, and still thinks a leg over once a week is appropriate?
You don't have any hope of getting him back and please for your own sake and the sake of your children, stop trying. You never really had this waste of space in the first place. You should go to Women's Aid and see if you could do the Freedom Programme, try to figure out why you have accepted this shit that has been dumped on you for so long, why you want more of it, and how to move on without him. 0808 2000 247
You need to start saying to yourself that you don't need him and you need to put a stop to the visits at your place. He can take the children out somewhere and bring them back the same day, with no sleeping over. It may be hard at first when you don't seem to believe it, but you cannot cure this man of his huge problems and he will end up destroying your self esteem as long as you keep on trying. Focus on yourself and your children.
Does he work? How did he have that sort of money to give to his mother?
Please go to your local CAB and ask how to go about divorcing him and getting child support. You could tell whoever you speak to about the money owed by his mother and see if there's any hope of seeing any of it again while you're at it.