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Everything you need to know and it is in the Old Testament.
1) The sins of the father are not passed onto the son.
2) The sinner that repents will live and not die.
"It is the one who sins who will die. A son is not to suffer because of his father's sins, nor a father because of the sins of his son. Good people will be rewarded for doing good, and evil people will suffer for the evil they do.
If someone evil stops sinning and keeps my laws, if he does what is right and good, he will not die; he will certainly live. All his sins will be forgiven, and he will live, because he did what is right.
Do you think I enjoy seeing evil people die? asks the Sovereign LORD. "No, I would rather see them repent and live.
"But if a righteous person stops doing good and starts doing all the evil, disgusting things that evil people do, will he go on living? No! None of the good he did will be remembered. He will die because of his unfaithfulness and his sins."
(Ezekiel chapter 18 starting verse 20)
The teaching of Christ is Christianity but the message of love and forgiveness and God's grace, blessing and Salvation run all the way through the whole Bible.
Salvation is for all generations, similarly the wages of sin is death.
People like yourself who quote from the Old Testament always select what happens to people who are disobedient. Really you should be looking to see what happens when people follow the Lord, then you will be able to say with the Psalmist, "Surely goodness and mercy shall follow me all the days of my life."
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