How can one deal with an ex-husband who refuses to leave the home of his divorced wife and her children, despite having become a stranger to them and the children hating him due to his violence?

If you own the house and the man has no right to it, you may prevent him from residing there. If he does not comply, refer the matter to a religious or civil judge. However, if the house belongs to him, he has the right to reside in it. But if your 'iddah (waiting period) has ended, you are not permitted to live with him, and he must provide housing for you and your children under his care. You may live with him in the same house on condition that there is no risk of temptation (fitnah) and that you have a separate part of the dwelling. A father's violence does not permit his hatred or disobedience.