Is it permissible for a father to view his children's messages without their consent, and is that considered spying?

The default is that it is not permissible for a Muslim to pry into the privacy of others, spy on them, or think ill of them. This is based on Allah Almighty's saying: "O you who have believed, avoid much [negative] assumption. Indeed, some assumption is sin. And do not spy," and on the Prophet's (peace be upon him) saying: "O community of those who have believed with their tongues, but faith has not entered their hearts! Do not backbite Muslims, nor seek out their faults. For indeed, whoever seeks out the faults of Muslims, Allah will seek out his faults, even if He exposes him in his own home." And also based on the Prophet's (peace be upon him) saying: "Indeed, if you seek out the faults of Muslims, you will corrupt them or be close to corrupting them." However, if a father knows about his children's illicit relationships, he has the right to investigate in order to deter them from wrongdoing. This is no less than the case of the Muhtasib (public morals enforcer) who is permitted to investigate and uncover those who commit sins.