Is it Islamically permissible for a husband to force his wife to live with and care for his children from his divorced wife, given that she has a sick daughter and the wife refuses out of fear of harm? And is the husband considered oppressive if he divorces her for not obeying him in this matter?

A husband does not have the right to compel his wife to live with his children from another woman, or to serve and care for them. She does not sin if she refuses to do so, because harm and detriment may befall her. The husband should not divorce his wife for refusing this, but if he is in need of this, then divorcing her is permissible. If the woman fears divorce, there is no impediment to her relinquishing some of her rights.