I have often heard it claimed that Brigham Young and the early church leaders did not understand that sealings were supposed to go from us back to our parents and then to their parents and so forth on back.
That is totally false, and here is the proof. He is discussing which ordinances the Lord will allow to be performed in the Endowment house since they had been driven from their temples, and which will require a new temple. And I might note, that Brigham Young understands it more than practically anybody I have talked to, as he understands that it is necessary for our sealings to link us back to Adam. Godhood is heriditary, so to speak, and we must be tied back to Adam, Adam and Eve being the Father's literal offspring.
This excerpt is from Brigham Young "The Ordinances, etc..." Journal of Discourses 16, discourse 24
"This we can do in the Endowment House; but when we come to other sealing ordinances, ordinances pertaining to the holy Priesthood, to connect the chain of the Priesthood from father Adam until now, by sealing children to their parents, being sealed for our forefathers, etc., they cannot be done without a Temple. But we can seal women to men, but not men to men, without a Temple. When the ordinances are carried out in the Temples that will be erected, men will be sealed to their fathers, and those who have slept clear up to father Adam. This will have to be done, because of the chain of the Priesthood being broken upon the earth. The Priesthood has left the people, but in the first place the people left the Priesthood. They transgressed the laws, changed the ordinance, and broke the everlasting covenant, and the Priesthood left them; but not until they had left the Priesthood. This Priesthood has been restored again, and by its authority we shall be connected with our fathers, by the ordinance of sealing, until we shall form a perfect chain from father Adam down to the closing up scene. This ordinance will not be performed anywhere but in a Temple; neither will children be sealed to their living parents in any other place than a Temple. For instance, a man and his wife come into the Church, and they have a family of children. These children have been begotten out of the covenant, because the marriages of their parents are not recognized by the Lord as performed by his authority; they have, therefore, to be sealed to their parents, or else they cannot claim them in eternity; they will be distributed according to the wisdom of the Lord, who does all things right. When we had a Temple prepared in Nauvoo, many of the brethren had their children who were out of the covenant sealed to them, and endowments were given. Then parents, after receiving their endowments, and being sealed for time and all eternity, and they have other children, they are begotten and born under the covenant, and they are the rightful heirs to the kingdom, they possess the keys of the kingdom. Children born unto parents before the latter enter into the fullness of the covenants, have to be sealed to them in a Temple to become legal heirs of the Priesthood. It is true they can receive the ordinances, they can receive their endowments and be blessed in common with their parents; but still the parents cannot claim them legally and lawfully in eternity unless they are sealed to them. Yet the chain would not be complete without this sealing ordinance being performed."