Is the husband obligated to leave his father and sister alone after the death of their mother and her dying wish concerning them, or should he separate from his wife and young daughter who refuse to return to live with his family, knowing that his family loves her and does not harm her, and that she fears that taking on the responsibility for his family will affect her happiness?

May Allah grant you comfort in your bereavement for your mother. Your wife has the right to live in an independent dwelling, and she is not obliged to live with your father and sister unless she agrees to it. She has the right to refuse to live with her husband's relatives if she is harmed by their knowing her private affairs.

If your wife does not agree to live with them, then find a solution for your father and sister's accommodation, such as their living with one of your sisters, or you renting a spacious dwelling for them.

Divorce should not be resorted to, as its consequences are dire. The default ruling on it is prohibition, and it is not permissible except out of necessity.