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.} [Fatir 35:18]
But if the father or mother commits a sin, this may be a cause of making the family members follow their example. (End quote from Majmu` Fatawa Ash-Shaykh Ibn Baz, 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.