Cain was not in Adams genealogy because Adam was not his father. Satan was Cains father.
To not list all the descendants of a person in the genealogy does not mean that those other children don't exist (See Genesis 5:4).
Ask a doctor. It is possible for a woman to be impregnanted by 2 different men at the same time giving birth to "twins".
The probablity of that is almost nil. But Satan did not "know" Eve in an intimate way, therefore, there is no possibilty.
And Adam knew Eve his wife; and she conceived, and bare Cain, and said, I have gotten a man from the LORD. (Genesis 4:1)
To include all the offspring of Adam in a genealogy would make the Bible one HUGE book. All people, not just some, descend from Adam. That means everyone on earth. Do you want the lineage of every single person on earth up to the time of Jesus to be included in the Bible? If not, you will have an incomplete list of Adam's descendants. And we have only three names of Adam's several children: Cain, Abel, and Seth.
"After Seth was born, Adam lived 800 years and had other sons and daughters." (Genesis 5:4)
The descendents of Cain still live today as God told Noah to bring 7 of every clean animal/race and 2 of each unclean. This includes the descendents of Cain known as Kenites. Just because Kenites are descended from Satan himself does not condemn them as they have free will as well and have to be given a chance to accept Christ. This is why God spared them from the flood.
Are you suggesting that some humans were clean and some unclean? There is no Bible that teaches this.
Genesis 7
8Of clean beasts, and of beasts that are not clean, and of fowls, and of every thing that creepeth upon the earth,
9There went in two and two unto Noah into the ark, the male and the female, as God had commanded Noah.
Clean beasts and unclean beasts are not humans.
All have sinned and in Adam all die. God made all men from one blood. Genealogy can't make a person righteous or unrighteous.
What you are attempting to teach with your serpent seed doctrine deals with British Israelism which a ridiculous hypothesis begun by a man named John Sadler. The white supremicists love this false doctrine.