Goodness OP - I do feel angry on your behalf - it sounds as though you have found your own anger, born from the pure frustration of having such a selfish person as your partner.
From what you say about his previous relationship it sounds he's learned nothing - or just doesn't care to. Because, look, he's got YOU taking up all the responsibility he should be sharing. Thank goodness you are NOT married to him and are in a good financial position.
You do need to be much more assertive though, because he is well and truly taking advantage of you. Also I believe he IS allowed to move out under these circumstances- where he moves to is his concern. Check the www.Gov.uk website. Living together such strained circumstances is not good for you, particularly as you are doing the lion's share of the work.
You should definitely not have to be finishing your work so late because he's such a selfish "look-at-me" manchild.
Today I'm going to try to have a nice day with DD and stepchild and ask him again when he's going to his dad's.
Actually don't ask him - TELL him. Give him a very short deadline (after his DC goes) and make him stick to it.
If you think he'll kick up a huge fuss then, last resort, pack his stuff up whilst he's returning his DC and leave it in a secure place for him. (Garage? Locked porch?) and keep the door locked until you are able to get the locks changed. I know you won't want to do this, though.
Glad you get on with his child's mother do you will still get to see them. Perhaps you are able to provide that DC with a tablet so you can video call them?
Whatever you decide good luck - I'm sorry you are being driven to this. 🌹