Praise be to Allah.
No person will be punished for the sins of another. Each person will be brought to account for his own sins. Allah says (interpretation of the meaning):
“And no bearer of burdens shall bear another’s burden”[Faatir 35:18]
But if the father or mother commits a sin, this may be a cause of making the family members follow their example.
Majmoo’ Fataawa al-Shaykh Ibn Baaz, 2/610
But the consequences of the sins committed by the sinner may go beyond him to affect his family, as a punishment for him and a test for his family. Allah tests man with disasters in order to expiate for his sins, and Allah may test people with blessings. Allah says (interpretation of the meaning):
“We shall make a trial of you with evil and with good” [al-Anbiya’ 21:35]
Whatever the case, the Muslim must avoid sin so that he will not be subject to the wrath and anger of Allah. And Allah knows best.