Can a mother be considered a dayyouthah if she knew about her daughters' conversations with strangers online and did not prevent them, knowing that this goes against her wishes?

Linguistically and technically, dayyathah (cuckoldry/lack of protective jealousy) is defined as a lack of gheerah (protective jealousy) over one's family and mahārim (unmarriageable kin). In the Sunnah, a dayyooth (cuckold/one lacking protective jealousy) is he who condones evil in his family, or who is indifferent to those who enter upon his family. Some scholars have limited the definition of dayyooth to one who condones zinā (unlawful sexual intercourse) in his family, while others have broadened it to include anyone who lacks gheerah over his family and condones reprehensible acts within them, such as tabarruj (immodest display) and ikhtilāt (unrestricted intermingling of sexes). Scholars agree that a dayyooth is one who has no gheerah over his household, and dayyathah is considered one of the major sins.

As for women, they are not described as dayyoothah (female lacking protective jealousy), but they must denounce evil according to their ability, based on the Prophet's ﷺ saying: "All of you are shepherds, and all of you are responsible for your flock." A woman is a guardian over her husband's home and her children. A woman must denounce unlawful conversations on social media, such as speaking in a soft, alluring manner or enticing to harām (unlawful acts), and it is forbidden to remain silent about such matters.