You miss-read my mind lol. I do not think it is a punishment from God. I think is a consequence of our actions. God is warning us because He is omnipresent and sees the results.
If we live a life that pleases God, our children and their children will be more likely to live a life that pleases God.
If I live a sinful life, it is more likely my children and their children will live a sinful life.
God judges us on our actions only, which is what the scripture you posted states.
I sin, therefore the sin nature is passed to my grandchildren and their children.
May God our father lead us to His truth.
And I would agree that as we all now live in a world that is well below paradise, we are subject to curses listed in Genesis that pre-fall Adam and Eve didn't encounter.
However:
One thing I am sure we can agree on: now that we know all have sinned and need a savior, let's share Jesus with them!