You are not morally or legally responsible after they grow up. You may be surprised to know that God respects mankind and the free will that He gave us. God loves His creation. That includes mankind, who are inclined not to reciprocate. God has made it possible for all mankind to be reconciled to their Creator. That does not mean that all mankind will accept God's provision. God will not coerce people. He could. Then God would be violating man's free will - which of course means that it would no longer be free.
God has taken responsibility as far as possible without overriding mankind's free will. And mankind's freedom has a use-by date. There won't be any free will once the day of judgement comes.
Firstly, how your kids turn out, is a reflection on your parenting, so yes, you are responsible for how the conduct themselves. You may not be legally responsible for them, but you are certainly morally responsible for them. In fact, I'm pretty sure there's a scripture for that.
Pro 22:6 Train up a child in the way he should go: and when he is old, he will not depart from it.
Secondly, God does indeed do whatever he wants, without any thought to man's so called freewill. That's why we have verses like this.
Gen 50:18 And his brethren also went and fell down before his face; and they said, Behold, we be thy servants.
Gen 50:19 And Joseph said unto them, Fear not: for am I in the place of God?
Gen 50:20 But as for you, ye thought evil against me; but God meant it unto good, to bring to pass, as it is this day, to save much people alive.
Gen 50:21 Now therefore fear ye not: I will nourish you, and your little ones. And he comforted them, and spake kindly unto them.
Special note: The above verse does not say "God allowed" or "God used it for good anyway" It say, God MEANT it unto good, which means he caused it. Wait, let me guess.... God is not responsible!
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