Is the woman who is completely separated and divorced obliged to observe ‘iddah in the marital home?
Question

The wife left and went to her family’s house without the consent of her husband. After going through khul‘ and separation, she wants to spend the ‘iddah period following divorce in her husband’s house. Is it permissible for the husband to not allow her to spend the ‘iddah period in his house, or will he be sinning? Please note that she has moved all her belongings to her family’s house, and she wants to do that in order to make life difficult for the second wife and her ex-husband.
Praise be to Allah.If khul‘ or divorce (talaq) in return for compensation has been completed, then the woman is divorced completely from her husband and her divorce comes under the heading of baynunah sughra; she has become a stranger to him, so it is not permissible for him to be alone with her, and she is not obliged to observe ‘iddah in his house, and he is not obliged to let her stay. But if they agree that she can observe ‘iddah in his house, there must be someone else there so that they will not be alone together, and she must cover in front of her ex-husband.
It says in al-Mawsu‘ah al-Fiqhiyyah (25/117): If the ex-husband’s house is spacious enough for both of them, and she can live in a separate room with a lockable door (and with all necessary facilities), whilst the ex-husband lives in the rest of the house, it is permissible. If there is no lockable door between them, but she has a mahram with her who can protect her from being alone with him, it is permissible. Otherwise, it is not permissible. End quote.
Al-Bahuti (may Allah have mercy on him) said: The woman who is completely divorced may observe ‘iddah wherever she wants in her city, in a safe place. She does not have to observe ‘iddah in his house, because Fatimah bint Qays narrated that Abu Amr ibn Hafs divorced her completely whilst he was absent, and he sent something to her but she did not like it, so he [‘Amr’s envoy] said: By Allah, you are not entitled to anything from us. She came to the Messenger of Allah (blessings and peace of Allah be upon him) and told him about that, and he said: “You are not entitled to maintenance or accommodation from him.” He told her to observe ‘iddah in the house of Umm Sharik, then he said: “She is a woman whom my companions visit; observe ‘iddah in the house of Ibn Umm Maktum.” Agreed upon."(Kashshaf al-Qina‘  5/434).
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) said: If he has issued a third divorce (talaq), and there is someone else in the house so that she will not be alone with the husband who divorced her, then there is nothing wrong with her remaining in the house, but she may move to her family’s house. But if there is no one in the house except the man who divorced her for a third time, then she must leave, because she is completely divorced from him and is no longer permissible for him. Based on that, it is not permissible for him to be alone with her. Therefore she must leave and go to her family’s house."(Fatawa Nur ‘ala al-Darb).
Based on that, you do not have to let her observe her ‘iddah in your house, because she is not entitled to accommodation.
In the case of one who is revocably divorced (first or second talaq), she should observe ‘iddah in the marital home, and it is not permissible to make her leave.
It says in Sharh Muntaha al-Iradat (3/206): The revocably divorced woman should stay in the house of her husband, but not in the case of mourning, such as the one whose husband has died. This was stated by Imam Ahmad. That is because Allah, may He be exalted, says (interpretation of the meaning):
{Do not turn them out of their [husbands’] houses, nor should they [themselves] leave [during that period]} [Al-Talaq 65:1].
It makes no difference whether the husband gave her permission to leave or not, because it is one of her rights during the ‘iddah, and it is a right ordained by Allah, may He be exalted. So the husband has no authority to waive any of her rights, just as he has no right to waive the ‘iddah. End quote.
And Allah knows best.