@Primrose, I am very sorry that you’ve had this terrible shock. Try to eat and keep yourself hydrated. You need to reach for the love and support of trusted family/friends.
It is likely that an OW has been on the scene for a while, and the house deal panicked him to make a move.
The fact that he hasn’t discussed any feelings of discontent with you, to try to work through them, indicates that he has been creating emotional distance to justify abandoning you. The fact that he keeps walking away from you confirms this.
He feels a sense of entitlement to cause this devastation. He has broken your trust and breached his loyalty, and has abruptly changed your life and the children’s lives. He has caused chaos in your housing situation, and is treating you with contempt by walking away when you try to talk to him.
Do not accept any blame for his appalling behavior and choices. He could have handled this differently. If he has been cheating, it is due to his weak boundaries and flaws in his character.
I would find my anger, take control, and tell him to leave now. He deserves a sharp consequence for dropping this bomb and for treating you and the children with such disrespect. Tell him that you no longer want to share space with him. He needs to be out of the house immediately while you process this great shock and try to gain your equilibrium.
At some point, sooner rather than later, you will need the support of individual counseling.