Is it permissible to open a house of mourning (a rented house) for specific days after a death, under the pretext that mourning is a Sunnah in Islam, and is doing so forbidden or not?

Consoling is a Sunnah. However, gathering for it in marquees or houses of mourning is disliked (makruh) or contrary to what is better (khilaf al-awla), and it becomes forbidden (haram) if it involves anything prohibited. The ruling on opening a house of mourning depends on what is intended by it.