Will a person enter Hell due to being raised on haram money from his parents, even if he was displeased with that money and performed acts of obedience?

The Hadith you are referring to is that which was narrated by Al-Tabarani in Al-Kabeer from Ka'b ibn Ujrah and Ibn Abbas (may Allah be pleased with them both), and its essence is that every flesh and blood nourished by unlawful earnings, the Fire is more befitting for them. Your upbringing from unlawful wealth does not harm you, nor is there any sin upon you as long as you are not pleased with it and it is not from your own earnings, due to Allah's saying: "And no soul earns [anything] except upon itself, and no bearer of burdens will bear the burden of another." You should continue to advise your parents gently and seek lawful sustenance. If all of your parents' money is unlawful, then it is not permissible to eat from it. However, if it is mixed or you cannot find another source, then it is permissible for you to eat from it, and that will not affect your acts of obedience.