Oh Lavender, I can see why you feel so beset from all angles. It must be awful to be getting the official advice that you can't stop him staying. If you can get a second opinion from Womens Aid that would probably be a good thing.
I understand TweedleDi's thinking about not staying in the house whilst he is there. This would be my first course of action - you could leave as soon as the DC were in bed and return as early as you like in the morning to get them up. I wonder if you feel that's Hobson's Choice, because of how useless he is with the children? Remembering how at one point you were entertaining going away with him so you could make sure the DC were looked after, it probably feels like a very hard alternative, but I certainly think you should consider it.
I have another idea which you could combine with staying elsewhere, or try as an alternative. I don't know if what I am about to suggest is sound advice or not, so more knowledgeable posters please feel free to jump in immediately and tell Lavender to disregard it. I wonder, though, if this would be a survival strategy:
The police have told you to look after your own personal safety. Could you put a bolt on the inside of your bedroom door? I know the place is rented, but if the landlord were to kick up a fuss about this, I think that is a small price to pay. Then let H know that your bedroom is your space and he is not to set foot in it - if he does, you will consider it a physical threat and will report it to the police. You can reinforce this by telling him he has refused to consider your feelings and your mental welfare by respecting your request that he stays elsewhere, and therefore you are within your rights to regard him as a threat. Teach the DC a special knock so that they can come in if necessary. The minute the DC are in bed, you lock yourself in your room and do not engage, no conversations through the door, nothing. Make your room your safe space - fill it with scented candles or fresh flowers or whatever you need, have phone/tablet, favourite books, stash of snacks bottles of wine - the full survival kit. So that as soon as the DC are not around, you spend not a second in his company. Any attempt of his to get through your door and you call the police - you need to let him know you will do that, and if he calls your bluff you have to follow through.
Sounds pretty shit, but if Womens Aid don't give you better advice and we are in the situation that you have to let him stay, it might work as a damage limitation strategy, and also to demonstrate your resolve to him.