Cultures are great ways to celebrate human diversity, however when they clash with Islamic values, they will most likely bring negative circumstances. Islamically, there is no obligation to live with in-laws.
In general, it is the duty of the husband to provide at least one private room where his wife can have her own privacy. This room should only be accessible to the husband and wife. No other family members.
Imam Abū al-Ḥasan al-Qudūrī (may God’s mercy be with him) writes, “It is incumbent upon him to house her in a separate building in which none of his family [members live], unless she chooses that (to live with other family members).” (Mukhtaṣar al-Qudūrī)
It should also be noted that one should try their utmost in cooperating and respecting in-laws.
In the least, a husband should provide, a basic separate accommodation for the wife, especially if he has the financial capacity to do so.
It might also be worthy to note that the Islamic duty upon any husband is to serve both his wife and parents. Living in a separate accommodation is not against any Islamic injunction. Despite living separately, serving and honouring parents can be rendered by constantly visiting parents, attending to their needs and maintaining ties with them.
Unfortunately, many cultural norms are a means of friction amongst family members. If one follows the Islamic instructions, one will certainly experience peace and harmony.