How can one atone for hitting and tying up one's father due to an illness that deprives him of his faculties, and for the resulting psychological distress?

Your tying of your father, if it was for his benefit and there was no other way, then there is no sin in it. As for your hitting him, it is an act of disobedience (to parents) and a clear sin. You must sincerely repent from it by increasing your supplications for your father, praying for him, giving charity on his behalf, maintaining ties of kinship from his side, and honoring his friends.