What is the ruling on a husband divorcing his wife with a single pronouncement while she is still in the marital home and does not wish to inform her family?

If the divorce is not the third and final one (i.e., not a triple divorce) and it is not a khul‘ (divorce at the wife's request with compensation), then the wife has the right to reside with you in the house during her ‘iddah (waiting period), and it is not permissible to expel her, for Allah Almighty says: "Do not expel them from their homes, nor should they leave, unless they commit a clear immorality." You may reconcile with her before the ‘iddah ends (which is at the end of the third menstruation, or upon delivery if pregnant, or after three months for those who do not menstruate). If you do not reconcile with her before the ‘iddah ends, then she is irrevocably divorced from you and is not lawful for you except with a new marriage contract, and it is not permissible for her to cohabit with you except under certain conditions. However, if the divorce completes the triple divorce, then she is irrevocably divorced from you with a major separation (baynunah kubra) and is not lawful for you until she marries another husband and he divorces her after consummating the marriage, and cohabitation with her is not permissible except under the conditions mentioned.