I think you are mistaken. Yes, Eve and Lucifer (who fell to become Satan) had a sexual union (eating the fruit), but it was only spiritual in nature, and not material.

When Adam and Eve fell, they were reborn as the 'children of Satan' because Satan's nature came to dwell in them. Also, because they were the original children, they were destined to become the progenitors of all humanity, and all humanity would inherit God's nature and lineage through them.

But because they fell, the opposite happened, and humanity descended from them are ALL of Satan's lineage. Satan has a claim on ALL descendants of Adam and Eve. That is why humanity bust be reborn through Jesus, and 'adopted'.

But, in order to reverse the fall and the corruption that happened, and restore humanity back to his lineage, God must take steps to slowly reverse the conditions the Fall created. Adam had a responsibility, so God cannot simply wave a magic wand and fix everything. Someone in the place of Adam must reverse Adam's mistake. To have faith in God's word when Adam had disbelief. To unite with God;s word to become the embodiment of Good, where Adam united with Satan's word to become the embodiment of Evil.

Note; There is no such thing as absolute evil. Only God and only Good are absolute. Evil is in fact the condition of having BOTH good and evil elements together. THAT is what evil is.

Because Adam failed, and came to have both good and evil within, he could no longer fulfill his responsibility. He failed. So God then CHOSE Cain the elder son to symbolize the evil in Adam, and put Cain in a position of relating to only one master: Satan. But he also chose Abel the younger son, to symbolize the good in Adam, and also stand in a position to relate to only one master; God.

For what purpose? To have the elder humble himself and unite with the younger, reversing the fallen actions of Lucifer towards Adam. IF Cain did this, "you will be received, but evil is crouching at your door, and you must master it." so clearly, Cain COULD have done it. but he also failed, like Lucifer.

So the real pattern and purpose behind the lineages in the Bible is to have a lineage that reverses the failure of Adam - by believing in God;s word and embodying goodness - which separates them from Satan's influence.

But the original and seed is the same: Adam's seed. Adam become a being of both Good and Evil, and so these must be separated, and this is done by raising lineages that CONDITIONALLY are able to represent good and lineages that conditionally represent evil.

it would be more accurate to state that X are lineages over which Satan has MORE claim, and Y are lineages over which God has more claim. But only the lineage of Jesus himself (i.e. starting from Jesus - he is the FIRST) is God's actual lineage. And we only have that spiritually, through the cross.

The second coming is necessary because just as the fall was a two stage process : Lucifer > Eve (in spirit) and Eve > Adam (in the flesh and spirit), salvation aka restoration also is a two stage process: First, rebirth through Jesus & the holy spirit (in spirit) and rebirth through the Second Coming (in the flesh).

That's powerful evidence why the offspring of Adam and Eve ARE all Satan's offspring, in the sense that Satan has the claim over them, and the lineage is evil (mixture of good and evil).

So what happened at the time of the fall?

There are always elements shared in a relationship. When Eve united spiritually with Lucifer in a spiritual sexual union, she inherited Lucifer fallen nature, and was 'reborn' as Lucifer's daughter. But when she united with Adam, then that union was BOTH spiritual and physical in nature, because Adam and Eve had both a spirit and flesh. Lucifer, only a spirit.

But from the point of the Fall onwards, Adam and Eve were no longer able to stand in the position of God's children. So they were ejected from the Garden, which symbolizes the realm of God's sovereignty. And, all their offspring are born of that fallen lineage. Until they are reborn through Christ into God's lineage.

The fall was indeed sexual in nature, because it was 'love' and Eve's love, symbolized by the fruit, was the means by which Lucifer / Satan gained control and authority over her. But it was not material in nature. Only spiritual.

Paul explains that even the first fruits (those reborn through Jesus) still await for 'adoption' - "the redemption of our bodies".

Satan surely has more influence and control over some bloodlines than others, and indeed, God purified the bloodlines in Israel as much as possible in order to be able to give birth to Jesus at some point.

But all who believe in Jesus and receive the holy spirit are reborn into Christ's spiritual lineage, and the rebirth of our flesh - the claim of Satan over our flesh - is to be liquidated when Christ returns.

The viewpoint that Adam and Eve fell to become of Satan's lineage, and that the mission of Christ is to restore God's lineage, will find a lot of corroboration in scripture.