What should the questioner do to avoid accountability, and is she obligated to do anything regarding her knowledge of her relative's adoption of two children 30 years ago?

The woman committed a grave sin by falsely attributing two children to her husband. This is an unlawful adoption, which Islam has forbidden to preserve lineages, in accordance with His (Allah's) saying: "Call them by [the names of] their fathers; it is more just in the sight of Allah." The man must deny anyone falsely attributed to his lineage; otherwise, he would be affirming falsehood. Sponsoring orphans is an act of piety, provided the sponsored child is considered a non-relative. You are not responsible for the actions of others, in accordance with His (Allah's) saying: "And no bearer of burdens will bear the burden of another," but you should have advised them if you were certain of the matter.