Is the female questioner sinful for allowing her ex-husband – whom she divorced due to his sexual deviancy – to temporarily reside in a separate room in her house, knowing that he has no shelter after losing his livelihood, and bearing in mind that he is the father of her children and she has no desire to return to him?

There is no sin upon you for accommodating your divorced wife in a separate room with its facilities in your house, so long as there is no khalwa (definition) (private seclusion) or fear of fitna (temptation). Al-Bahuti permitted this in cases where the house is spacious enough, and it is possible for each of them to live in a separate place, such as a room or an upper floor, with a door that closes between them, or if each of them has an independent space where one does not see the other, and she is accompanied by a mahram (definition) who protects her.