Ok well I'm going to give a different opinion to all here saying call the police to have him dragged out of your (joint) kids' bedroom in the night here.
Yes, that would be deeply traumatic for the children and would be imo completely OTT.
You haven't said why you're splitting up. Nowhere have you said he's dangerous/abusive/violent etc. Has this decision come out if the blue for him? His house is not habitable. He has not said he won't go. He's said give him a moment to sort something out - with his brother, etc.
And why are people here immediately going crazy? 'I wouldn't let him sleep with the kids!!!! Are they his?!!!' - this is just so reactionary. We have barely any details here. They are his and your children, and you haven't said anywhere he's a bad or dangerous father.
Why shouldn't he sleep in a room with the children?? You've asked him to go. You don't want him. This means he'll also have to go away from his children. We don't know the details but presumably that will be an awful separation for them and him. He isn't imposing himself on you but why should you feel you can order him to sleep on the sofa 'but' he's going in with the kids? They are not just your kids. ! He's about to move out! Why shouldn't he be close to them for a few days? How anyhow is this separation going to be dealt with as far as they're concerned?
I'm sorry but he's said he'll go and possibly is just keeping things normal I presume FOR THE KIDS while he deals with the shock and gets himself organised with somewhere to go.
Don't listen to some of the rubbish on here. Talk to him like the co parent you are about how this is going to be presented to the kids. Focus on minimising their stress. Let him gently go when he's sorted out somewhere - not an hour's notice and he's dumped on a building site.
Of course we don't know WHY you're leaving him and how he's behaved. That may change my opinion completely. But if you're just fed up with him but he isn't bad or dangerous, then personally I think it's only fair and best for all to deal with this in a civilised way.