Salvation is an individual matter, and if a person who has been born under the covenant rebels and denies the Lord, he will lose the blessings of exaltation. Every soul will be judged according to his works and the wicked cannot inherit eternal life. We cannot force salvation upon those who do not want it. Even our Father's children had their agency before this life, and one-third of them rebelled.
It is the duty of parents to teach their children so that they will walk uprightly and thus obtain the blessings of their birthright.
But children born under the covenant, who drift away, are still the children of their parents; and the parents have a claim upon them; and if the children have not sinned away all their rights, the parents may be able to bring them through repentance, into the celestial kingdom, but not to receive the exaltation. Of course, if children sin too grievously, they will have to enter the telestial kingdom, or they may even become sons of perdition.
When a man and a woman are married in the temple for time and all eternity and then separate, the children will go with the parent who is justified and who has kept the covenants. If neither of them has kept his covenants, the children may be taken away from both of them and given to somebody else, and that would be by virtue of being born under the covenant.
(Book: "Doctrines of Salvation," 1954-1956, vol. 2, p. 91)