What is the ruling on living with two people, one of whom provokes others with words, demeans them, and associates with those who abandon prayer, and the other imitates disbelievers, neglects Fajr prayer, and is characterized by a lack of manners?

The Messenger of Allah (peace be upon him) forbade entering the dwellings of those who were punished, except while weeping, for fear of being afflicted by the punishment. Likewise, caution must be exercised when associating with wrongdoers and immoral people. One should not associate with them unless it is in a manner that protects the Muslim from punishment, and the least of that is to denounce their actions. Associating with immoral people is permissible in two situations: 1. Compulsion (ikrah). 2. When there is an overriding religious benefit that outweighs the harm of association, or to avert a greater harm.

So, if you are denouncing their actions and advising them, then there is no harm. Otherwise, it is not permissible to live with them except out of necessity. You must distance yourself from evil as much as you can.