Your making sense, I agree, that my actions may have consequences on my children and so forth, I agree.
I disagree thought that this type of 'consequence' is what the passage is speaking of, reason being, the passage clearly distinguishes from the Love and Hate. Look if you will:
...punishing the children for the sin of the fathers to the third and fourth generation of those who hate me, but showing love to a thousand generations of those who love me and keep my commandments.
So for example, if we have a German family, who is Christian and loves God, does this mean they will not be 'consequently' punished, and have no prejudgement on them? Because in this passage it says God punishes those who hate Him.
As you have stated:
The child is not being punished for the mothers action, but the mother's action is having a consequence, which is affecting her child (can you see the difference?)
Such consequences are not PUNISHMENTS, but rather a set up, for example, when Abraham, peace be upon him, was told to sacrafice his son, peace be upon him, his son, was not being punished but tested. So although God loved them, he tested them.
This is why I don't take the passage to mean 'consequential' stuff.
Punishment, is rather like the executions that we read in Numbers of the 'boys' and 'children' the 'females who had slept with man', their killing, by God's people, when their killing was not needed, that was Punishment, not because of the Boy's sin.
Peace.
Peace be upon you too.
May Abraham, Moses and Jesus, be immune from any lies ascribed to them, May they be granted peace and blessings and also upon their followers.
Any mistake is mine, any good then praise be to the God of Abraham.