What should a religious young man do who faces problems with his parents who have wronged him, and he is unable to seek their forgiveness due to his father's harshness and his inability to speak with him, while he can please his mother but fears losing his father's approval?

You must treat your parents according to what Allah has enjoined upon you in His Book, by showing them kindness, obeying them in all matters that do not involve disobedience to Allah, and accompanying them with goodness, even if they treat you poorly. This is based on the Almighty's saying: "And We have enjoined upon man [care] for his parents. His mother carried him with hardship upon hardship, and his weaning is in two years. Be grateful to Me and to your parents; to Me is the [final] destination. But if they endeavor to make you associate with Me that of which you have no knowledge, do not obey them, but accompany them in [this] world with appropriate kindness." There should be no problems between you and your parents, nor should they remain displeased with you. You must strive to gain the satisfaction of both of them, not just your mother.