There were no sealing rituals between parents and children in Joseph Smith’s life time.  In his August 13, 1843 speech the prophet explained why such sealings were unnecessary: ”A measure of this sealing is to confirm upon their head in common with Elijah the doctrine of election or the covenant with Abraham—which which when a Father & mother of a family have entered into their children who have not transgressed are secured by the seal wherewith the Parents have been sealed.”  Parents who were sealed to each other would have the opportunity of having their children sealed to them also so long as their children did not “transgress.”  Therefore, no additional ordinance was necessary. Howard and Martha Coray’s much notes make it clear that William Clayton’s much briefer notes (just a few sentences) were problematic. ”When a seal is put upon the father and mother it secures their posterity so that they cannot be lost but will be saved by virtue of the covenant of their father.”  Again, Clayton’s notes were extremely truncated; researchers need to look to more thorough notes to get a better sense of Joseph Smith meaning (like Elder Bednar did).
Joseph Smith did teach antinomianism but like all other antinomians (from the heresy of the free spirit to John Dee to John Humphrey Noyes) perfection and thus being above the law was something that one achieved. One progressed to that stage. Doctrine and Covenants 132 makes this clear: “if ye abide in my covenant” (19). Joseph Smith did perform the second anointing, but this was only given to those he felt had proven their faithfulness. It was not given to children or newly baptized members.
That is, there isn’t any special ticket to the Celestial Kingdom for children of righteous parents. Smith did teach that the righteous had the ability to save/exalt others in his King Follett Discourse. But this ability did not only apply to children, this applied to everyone, friends included, that the righteous wanted to save. ”Every spirit can be ferreted out in that world that has not sinned the unpardonable sin neither in this world or in the world of spirits. Every man who has a friend in the eternal world who hath not committed the unpardonable sin you can save him.”  Again children didn’t get any special benefits that didn’t apply to everyone else. Children simply were afforded the sealing rite without an ordinance (which would become effective if they were righteous) whereas sealings to non-relatives required an ordinance.
Smith’s statement in the King Follett Discourse suggested the broad scope of who could be saved: everybody who had not committed the unpardonable sin. Taken to it’s logical conclusions, this (as J. Stapley rightly alludes to) takes us back to DC 19. Suffering will be severe but temporary. This applies to all people. This was a classic statement of Universalism. As the Universalists were want to say, the love of God would eventually (after much suffering for the wicked) bring everyone back. Such would not override agency, because no one would refuse God’s love for ever, the Universalists believed. Eventually (again after much suffering for the wicked) all would choose God; it just made sense.  DC 76 and the statement from the King Follett Discourse cited above made it clear that Smith was a near-universalist rather than a full one–the sons of perdition would not be saved–but Smith’s revelations were still pretty broad.
Such helps to contextualize Orson Wintney’s now much-quoted statement. ”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.” While this applies to the children of the righteous, DC 19 makes it clear that it also applies to everyone else. That is, we all have a righteous Father calling us to return.
1 Jonathan Stapley, “Adoptive Sealing Ritual in Mormonism,” Journal of Mormon History 37, no. 2 (2011): 59.
2. August 13, 1843, Words of Joseph Smith, 241.
3. I don’t think this was a reference to any sin whatsoever, but just indicated that children needed to be generally righteous for this to work.
4. August 13, 1843, Words of Joseph Smith, 242.
5. April 7, 1843, Words of Joseph Smith, 360. Smith didn’t make it clear what kingdom such saved people would end up in, but those with ideas similar to Smith (particularly Jane Lead) said that souls would slowly advance through the various heavens, as they purged themselves of their sins. Perhaps Smith also believed in advancement through kingdoms.
6. D. P. Walker, The Decline of Hell: Seventeenth-Century Discussions of Eternal Torment (Chicago: University of Chicago Press, 1964). Joseph Smith’s grandfather was a Universalist.