Do my married brothers have a right to my deceased father's house, which my mother, sister, and I inhabit, knowing that they use it with complete freedom without regard for our privacy?

If a person dies, their ownership transfers to their heirs. If they agree not to divide the inheritance, there is no sin. If the house is rented, your brothers have no right to it. As for the furniture in the house, it is the property of your father, so your brothers have a share in it. You can acquire it by compensating them or by buying their share, or it can remain shared.

Permission must be sought before entering the home of its occupants, even if the brother lives with them or owns a part of the house, because the Prophet, peace and blessings be upon him, said: "Ask permission to enter upon her. Would you like to see her naked?" And Allah Almighty says: "O you who have believed, do not enter houses other than your own houses until you ascertain intimacy."

So, your brothers do not have the right to violate your privacy in the home, and they must respect your resting times. If the non-division of the inheritance or the house furniture gives them a justification for this, then it is better to divide everything that is shared to prevent any harm resulting from sharing.