Approach children with reason, with persuasion and love unfeigned

"Fathers, if you wish your children to be taught in the principles of the gospel, if you wish them to love the truth and understand it, if you wish them to be obedient to and united with you, love them! and prove to them that you do love them by your every word or act to them. For your own sake, for the love that should exist between you and your boys—however wayward they might be, or one or the other might be, when you speak or talk to them, do it not in anger, do it not harshly, in a condemning spirit. Speak to them kindly; get them down and weep with them if necessary and get them to shed tears with you if possible. Soften their hearts; get them to feel tenderly toward you. Use no lash and no violence, but … approach them with reason, with persuasion and love unfeigned."

- Joseph F. Smith, Teachings of Presidents of the Church: Joseph F. Smith, (2011), 249–55
http://www.lds.org/manual/teachings-joseph-f-smith/chapter-28?lang=eng

When parents keep the covenants they have made at the altar of the temple, their children will be forever bound to them

"It is not uncommon for responsible parents to lose one of their children, for a time, to influences over which they have no control. They agonize over rebellious sons or daughters. They are puzzled over why they are so helpless when they have tried so hard to do what they should.

"It is my conviction that those wicked influences one day will be overruled.

"'The Prophet Joseph Smith declared—and he never taught a more comforting doctrine—that the eternal sealings of faithful parents and the divine promises made to them for valiant service in the Cause of Truth, would save not only themselves, but likewise their posterity. Though some of the sheep may wander, the eye of the Shepherd is upon them, and sooner or later they will feel the tentacles of Divine Providence reaching out after them and drawing them back to the fold. Either in this life or the life to come, they will return. They will have to pay their debt to justice; they will suffer for their sins; and may tread a thorny path; but if it leads them at last, like the penitent Prodigal, to a loving and forgiving father’s heart and home, the painful experience will not have been in vain. Pray for your careless and disobedient children; hold on to them with your faith. Hope on, trust on, till you see the salvation of God.' (Orson F. Whitney, in Conference Report, Apr. 1929, p. 110.)

"We cannot overemphasize the value of temple marriage, the binding ties of the sealing ordinance, and the standards of worthiness required of them. When parents keep the covenants they have made at the altar of the temple, their children will be forever bound to them."

- Elder Boyd K. Packer, Of the Quorum of the Twelve Apostles, "Our Moral Environment," General Conference, Apr 1992
http://www.lds.org/general-conference/1992/04/our-moral-environment?lang=eng

We will save our posterity

“If you succeed in passing through these trials and afflictions and receive a resurrection, you will, by the power of the Priesthood, work and labor, as the Son of God has, until you get all your sons and daughters in the path of exaltation and glory. This is just as sure as that the sun rose this morning over yonder mountains. Therefore, mourn not because all your sons and daughters do not follow in the path that you have marked out to them, or give heed to your counsels. Inasmuch as we succeed in securing eternal glory, and stand as saviors, and as kings and priests to our God, we will save our posterity.” 

- Lorenzo Snow, Ensign, Sep 2002, p. 11
From Collected Discourses, comp. Brian H. Stuy, 5 vols. [1987–92], 3:364.
http://www.lds.org/ensign/print/2002/09/hope-for-parents-of-wayward-children?lang=eng&clang=eng

Parents do good and children will be yours forever

"Let the father and mother, who are members of this Church and Kingdom, take a righteous course, and strive with all their might never to do a wrong, but to do good all their lives; if they have one child or one hundred children, if they conduct themselves towards them as they should, binding them to the Lord by their faith and prayers, I care not where those children go, they are bound up to their parents by an everlasting tie, and no power of earth or hell can separate them from their parents in eternity; they will return again to the fountain from whence they sprang ."

- Brigham Young, Teachings of Presidents of the Church: Brigham Young, (1997), 170–76
http://www.lds.org/manual/teachings-brigham-young/chapter-24?lang=eng