What is the ruling on informing the father about his divorced sister, who is more than 15 years older, leaving the house and about her illicit relationships, knowing that he is ill and this might cause him distress?

If informing the father about his daughter going out at night in a suspicious manner does not help prevent the wrongdoing and causes him harm, then informing is not obligatory. The obligation is to strive to prevent this wrongdoing to the best of one's ability, and to prevent her from going out if possible, while being keen on advising her, reforming her, reminding her of Allah and the Hereafter, seeking assistance from righteous female relatives, and supplicating abundantly for her guidance and repentance. It would also be preferable to strive to get her married.