Is a child obligated to correct his parents' sins?
I assume you are referring to an adult child. A child who is still a minor, and therefore subject to his parents' authority, cannot reasonably be assumed to have an obligation to correct his parents. As for an adult child, it would depend on the circumstances and the nature of the sin.
With a minor sin, it might be better for an adult child to trust that his parents can take responsibility for examining their own conscience. If the sin is serious, and especially if it directly impacts the adult child and his or her own family, then the child might need to talk to the parents about the matter. If possible, it would be appropriate and respectful for the child to ask questions about the behavior in question and the parents' intentions rather than to make accusations.