He does have somewhere to go.
He's a solvent adult. He can go to a hotel or b&b while he looks for a place to rent. Or he can go to parents or friends while he does the same.
The people who REALLY have nowhere to go are your children. At the moment they are living with a man who can be violent with little warning. You are in charge of who they live with. They depend on you for a safe environment, and have no alternative choice to what you decide.
Put them before him.
You DON'T have to make this public in order to get the help you need to get him out. Please please please call the non-emergency number and TALK to someone there. Ask their advice. They will be able to help you get him out of YOUR home without fuss, without violence - and keep you safe. The equivalent of you being able to hiss in his ear: 'Get out, NOW. Go quietly with these lovely people before I expose you for what you are, to everyone.'
And I would think that unless he is a very stupid person, he will go, tail between legs, and leave you alone.
Right now he is working his socks off to gain sympathy. Nowhere to go. Hang dog looks. Staying out of your way. It's all as CALCULATED as it can possibly be. He's not sorry, however.
You need to hear that repeated: HE'S NOT SORRY.
That translates as he thinks what happened is ok. So if you do not get him out and end this situation NOW, very soon you will find yourself back here. Maybe describing how one of your children saw him pushing you. Or worse.
You really really need to find a way to step up and protect them and get him out of the house. Please call the police.