The doctrine that parents are at least partially responsible for the acts of their children is clearly taught in latter-day scriptures. In fact, as is indicated in the following scripture, parents are responsible for the sins of their children if the parents do not teach them the gospel:
And again, inasmuch as parents have children in Zion, or in any of her stakes which are organized, that teach them not to understand the doctrine of repentance, faith in Christ the Son of the living God, and of baptism and the gift of the Holy Ghost by the laying on of the hands, when eight years old, the sin be upon the heads of the parents… .And they shall also teach their children to pray, and to walk uprightly before the Lord. (D&C 68:25, 28.)