How can one advise parents to abandon a certain sin or transgression when direct advice, books, or gentle counsel prove ineffective? And is it better for the person to only examine their own faults and sins and just pray for them?

Advice should be given through gentle speech or writing. If this does not work with the parents, an influential relative can intercede. If that is not possible, one should pray for them. It is not permissible to spy on their faults.