To what extent are parents responsible for the mistakes of their adult children, especially concerning their negligence in prayer and their wearing of immodest clothing?

Fathers are responsible for raising their children, especially when they are young, because the impact of upbringing at this stage is stronger. Furthermore, they are entrusted with their children. Ibn Qudamah likened a child to a plain jewel that can be engraved with anything. If accustomed to good, he will grow up upon it and share the reward with his parents and educator. If accustomed to evil, he will grow up upon it, and the sin will fall upon his guardian. One of the fruits of good upbringing is for parents to see their children in obedience to Allah, for nothing is more pleasing to a Muslim's eye than to see a child obedient to Allah. Among the most dangerous matters is neglecting prayer, and the Shari'ah has encouraged raising children upon it when they are young. It is not permissible to use anything that prevents water from reaching a limb during purification.