(Working on getting more quotes and sources but wanted to get out what I have so far of what I’ve been learning)
Bloodlines have to do with legally authorized blessings more than DNA.
Authorized baptism is, for all who are not already of the bloodline of Israel, adoption into the house of Israel, & as a son/daughter of Jesus Christ. Christ becomes the covenant father, and the bloodline is changed into the house of Christ. When a person is converted & baptized, their bloodline changes to that of Israel, and they become full heirs of all blessings of that house. They are assigned to a labor in one of the 12 houses of Israel, and look forward to all blessings related to that house. If they or anyone else of Israel forsake their covenants, they lose all blessings thereunto appertaining.
When we are sealed to someone in the temple they become our bloodline. They still have different DNA, but as far as the blessings of God to the seed are concerned, they are now your bloodline. They now share your ancestry. This is true for legal adoptions and temple sealings of those children into their adopted family.
A person may have multiple fathers and mothers in the millennium and eternity. Joseph Smith taught this, and he referred to more than just ancestors, but to having multiple mothers and fathers.
Here is an account to illustrate the adoption through sealing: Jedediah Grant’s son Heber J Grant (a president of the church) was a son of Joseph Smith by virtue of his mother being sealed to Joseph Smith. Heber saw a vision of a counsel in heaven of who was to fill a vacancy in the quorum of the 12 Apostles. He saw Joseph Smith say he wanted one of his sons to represent him in that counsel. Jedediah then said ‘yes, why not have the boy who bears my name who is your son be chosen?’ Then Heber recognized this as why he was selected. Though Joseph Smith was not the father of his flesh, he became his father by bloodline according to the sealing.
In the full order of the priesthood, people are sealed to the head of that dispensation as their father, in addition to being sealed to their father and mother that raise them. This would be true of those in the dispensation of Adam, Seth, Noah, Enoch, Melchizedek, Abraham, Moses, Peter, Nephi, etc. I understand that all dispensation heads are sealed to Joseph Smith as the gatherer of all things in one in Christ in the last days.
There was an order of family in pre-mortality, and temple sealings can help re-create that perfect order. This does not negate the fact that we are all literally children of God. Perhaps it suggests that there were certain groups of people in pre-mortality who clustered together based on similar views & ambitions, who were eventually ordained to be family in eternity, many of whom would also be family in mortality.
The Levirate law is that when a man dies, someone of his bloodline, typically his brother, enables his wife to continue having children. The children thus born are the sons of the deceased, and in eternity, the man sealed first to that woman has her for eternity. This is a selfless offer on part of both the man and wife. Christ taught of a situation where a man was sealed to a woman, who died, and she married her brother, and so on several brothers who died. The woman belonged only to the first man, and the others were merely helping to build his kingdom in his absence.
Brigham Young was sealed as a son of Joseph Smith. Other early brethren were too, and it was said that they were of the “Smith family” in pre-mortality. It might well be considered that Brigham thus has two fathers, namely Joseph, and the father of his flesh if he was qualified for that sealing. He then became of the same bloodline. After Joseph’s death, Joseph’s wives were then married to Brigham so Brigham would raise seed to the house of Joseph, Brigham being the bloodline of Joseph by virtue of the sealing. The seed from these arrangements are the seed and literal bloodline of Joseph. It might be considered that the children of such would be sealed to both Brigham and Joseph, having two fathers.
Plural marriage of multiple women to one man is also in accordance with celestial law when the keys of that ordinance are in effect. Even though plural marriage is not currently in operation in the church today, if a woman who was sealed to a man for time and all eternity dies, her husband may be sealed to another woman for time and all eternity. President Russel M Nelson is an example of someone in this situation.
There are not situations where a woman has multiple husbands in eternity, though she may, when the keys to such are operative, raise seed to her deceased husband with another of his bloodline. If the husband of a woman dies, she is ineligible to be sealed to another man for time and eternity, but only to be sealed to him for time.
Parents who do not remain faithful to temple covenants do not have right to those children in eternity. Only family relations sealed in temples are in effect in the next life. (I’ve written more on this topic in the parenting book.)
One could ask: Was not Joseph Smith sealed to a woman who was already married? He was, but it was not meant to be that way. Joseph was commanded to ask her to be a plural wife years prior before she was married, but he feared, and waited. It is also noteworthy that this woman had repeated dreams of marrying Joseph. Eventually she obtained a witness after Joseph asked her for marriage that it was of God, and she consented to the sealing. It is noteworthy that the man she was already married to was not opposed to the sealing, refused to join the church, and would not be involved with her in eternity. The man was also sealed to Joseph as one of his sons, which might offer him opportunity to great blessings within the scope of what he is willing to receive.
What of Mary the mother of Jesus? She is sealed as the wife of Heavenly Father. She was married to Joseph only for time. Sources say Joseph was an older man who already had a family of his own when he betrothed Mary. The Book of Mormon says Mary was carried away by the Holy Ghost for a time. During this time, she was married to Heavenly Father, and conceived the Christ child by him. She then returned to earth, and 9 months later had the holy child. She pondered these things in her heart. Joseph essentially fulfilled the Levirate law for Heavenly Father, raising seed to him through Mary via the children from that temporal marriage forthcoming. Mary is the wife of Heavenly Father in eternity, not Joseph.
Was Jesus in a Plural Marriage? There is great evidence that Jesus was married to at least two woman during his mortal life: Mary and Martha.The wedding where he turned water into wine was likely his own. He was likely in the home of Mary and Martha teaching them because he was married to them, otherwise this would be scandalous. There are many other evidences. See, for example, “Hidden Bloodlines” by the Joseph Smith Foundation, and my notes on such elsewhere in this text.
Was Plural Marriage practiced in the Book of Mormon? There are many references indicating that the great patriarchs of that book had multiple wives, including mentions of “wives” of these men. We also see that they had many children, too many for one wife, particularly in the Book of Ether. The rule of thumb is indeed monogamy, but not so for the holy celestial order. The Book of Mormon was written to a fallen audience, and didn’t need to be concerned with expounding this principle. See the full essay on this elsewhere.
It is important for individuals to marry in the covenant as it preserves the holy royal bloodline of Israel. Marrying outside of the faith or outside of a temple for any reason excludes someone from the holy inheritance of God wherein they become joint heirs with Christ, and receive all the father has, becoming Gods in eternity with a never-ending posterity, and crowns, thrones, kingdoms, and worlds without ends in their command.
Overview of all fathers a person can have: Once adopted to the household of faith in Christ, we then have both Heavenly Father and Jesus Christ as Fathers. If the father of our flesh remains faithful to his temple covenants, he is another of our fathers in eternity. Another father in eternity is the head of the dispensation to which we pertain. These are the several kingdoms to which a person may belong to in eternity. They are his houses. Naturally, a faithful person is authorized to begin their own kingdom as well. Adam, the head of all dispensations on this world under Christ, might well be added to this list. The list might go on much further than this, though perhaps these are those to whom we are direct descendants in 1 generation by virtue of the sealings.
Is Plural Marriage an Eternal Law? From what I can tell based on the teachings of Joseph Smith, scripture, and other prophets, though not currently authorized, plural marriage is the standard of the celestial kingdom. It is a higher law. Those who practice it without priesthood authority are in a state of apostacy and do so to their condemnation. As noted earlier, the Book of Mormon says the standard is monogamy, but we also read that narrow is the way to eternal life. That book was also written to a fallen audience concerned with living any law at all. Yes, most will not enter plural marriage in eternity. But it is the standard of the exalted. The D&C is clear that this order is the way to populate worlds without end. Joseph Smith and other mighty prophets have also been clear in their teachings on this subject.