In short, no.

This question arises from a misinterpretation of an LDS scripture, found in the Doctrine and Covenants.

The scripture is D&C 68:25:

"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."

The opinion I have, which was also taught by a religion professor at BYU when I took a D&C class, is that "the sin" refers to "the sin of not teaching the children", not "the sins of the children".

Hence the parents are answerable for *a* sin, but not the sins of the children.