Genetic Transmission
Are our children effectively our reincarnations since they share the same DNA and live on after we pass?
Apples and oranges. Or in this case, DNA material vs. spiritual material.
We choose our lifetime based on the arc of our journey. We choose our parents, choose our journey so that we can learn, teach, or fulfill some aspect we want to learn or fulfill. In most cases, we only bring about a third of our conscious energy to a lifetime - and two thirds is always "back home" (afterlife) observing what that other third is doing here while incarnated.
That conscious energy may have chosen a parent based on the DNA of that individual. Going to grow up "big and strong" or going to be "not strong, suffer from a hereditary disease" so that they can learn lessons from that experience.
Indeed, our children carry our genetic information - but they don't carry our consciousness. They may know us from previous lifetimes, they may have agreed to participate in this one for some reason based on those previous lifetimes - or they may have come with us for what is going to happen to them in the future. So on one level - if they have incarnated with us before - or are part of the group we "normally incarnate with" then indeed - they would be considered "a continuation of what we've all been working on."
These soul groups have some specific theme they're working on. (Could be courage, compassion, addiction, forgiveness, etc). So it may be that everyone from our soul group or classroom - is working on the same kinds of things. In that case, if our children are part of our soul group, they may have chosen us because our influence will allow them to explore that avenue. The place we choose to live may help them explore that avenue.
Both nurture and nature have a role in everyone's life. But there is that third aspect that science ignores, that religion doesn't appear to comprehend, that we choose our lifetimes to learn or teach lessons that we've signed up to learn.
Our souls are huge energy clouds, spanning through many dimensions, only a small part of this energy is incarnated in a body. The soul can not be 'captured", unless you give permission; however, you can lose parts of this energy in traumatic events, or a soul which lived in a body can get stuck in lower planes of reality as a ghost after death and needs to be rescued by Guides or Angels. Other people can also steal some of your energy. In shamanism, they do "soul retrieval" - returning these lost soul parts into the body. You can also have 'entity attachments" - when a discarnate being can attach to your energy field and affect your life, some people start hearing voices, etc. There is also "possession" of different degrees, typically overshadowing or psychic vampirism.
Aspects of your soul can go missing or dissipate or hang around certain places; while you are alive or in the afterlife. This is due to frequent fragmentation as a preferred method of defense mechanism.
Also, there are voodoo and shamanism practices that will enslave souls. When a person is vibrating low and also as once the soul dissipated or thinned out, the spiritual defense is reduced and imprisonment of the soul can take place by dark lords / dark task force.
Another example is when a deal is made with dark forces, they can and will come collect your soul that you have used as bartering token.