Does repentance prevent the sin from befalling the sinner's family later, based on the principle of "as you judge, so shall you be judged"?

The hadith (definition) "as you judge, so shall you be judged" (كما تدين تدان) is not authentic. Al-Trabelsi mentioned that its chain of narration includes someone accused of fabrication, and it was deemed weak by Al-Manawi and Al-Albani. There are other weak hadiths with the same meaning. Quranic texts such as "And no bearer of burdens will bear the burden of another" (وَلاَ تَزِرُ وَازِرَةٌ وِزْرَ أُخْرَى) indicate that the sinner alone bears the consequences of their sin. There is no authentic evidence to suggest that one of the consequences of a sin is that the same sin will be committed by the sinner's family. A sincere penitent is hoped to not be held accountable for their sin, neither in this world nor in the Hereafter.