Are the aforementioned reasons—such as housing disputes, the wife's backbiting, her false accusation against the husband's father, and her family's unreasonable demands and threats—considered legitimate grounds for divorce in Islamic law?

Divorce is the last resort and should only be pursued when cohabitation becomes impossible. If the situation of the wife and her family is as described, then there is no blame upon the husband for separating from her. In fact, divorce may be the most appropriate option at that point, given the impossibility of cohabitation and the failure of reconciliation attempts, in accordance with the Almighty's saying: "But if they separate [by divorce], Allah will enrich each of them from His abundance. And Allah is ever Encompassing and Wise." Divorce is permissible when there is a need for it due to the wife's bad character and ill-treatment, and it is recommended when she neglects her obligatory duties to Allah or her chastity.