Urgh.. he sounds like a fuckin' treat..
Don't let him back in the house if you aren't there (ie the suggestion that kids stay home, you stay with his mum whilst he stays at home with them) - at some point it is going to dawn on him that being IN the house would have been the better move... so do NOT let him back in!
ASK him how he wants to work 50/50 care - don't try to suggest things, ask him what HE wants to do. Make it look to the kids and to his mum like you FULLY embrace him having them with him, wherever he is living 50% of the time including overnights, school drop offs and pick ups etc etc. Do not let on that you do not want this!
Theres a really strong chance that he will piss about, realise he does not want this and you'll get what you want, but if you start setting out sensible ideas and practical routines that work for you now he will likely do his damndest to do anything but!
Put the ball firmly in his court, appear willing and eager to work with him as this will go in your favour far more than anything else will!
Speak to a legal bod asap!
This is really shitty of him but hopefully it won't be long before he realises how much work having the children 50/50 actually would be, that he can't actually do that with his work hours, and your solicitor will make it clear to him he cannot actually fuck off, evict you and the kids from the house and tra la la, be a free man doing as he pleases!