What is the legal ruling regarding the father of the wife demanding that she be provided with independent housing, despite the husband being aware of the husband's difficult circumstances, and the wife refusing intimacy until housing is secured, knowing that the wife lives with the husband's family in the same house without problems?

An independent dwelling is the wife's right, and it should be commensurate with her circumstances and the husband's financial capacity. If the husband is still in straitened circumstances and the wife is content with her situation, her father should not interfere. If the wife (who is an adult and of sound mind) willingly relinquishes her right to an independent dwelling, then that is her prerogative, and her guardian has no right to compel her to demand it. The wife's obedience to her father is not obligatory in matters that would cause her harm. As for her abandoning the marital bed when the husband does not fulfill her rights, there is no blame upon her for that. If reconciliation is not achieved and cohabitation becomes impossible, divorce may be preferable, for "And if they separate [by divorce], Allah will enrich each of them from His abundance. And ever is Allah all-Encompassing and Wise."