Why God punish children for the sins of their parents?
You ask a hard question and I'm going to try to help. God judges us on what we do. We will all stand before God and give an account. For some it will be unto judgement. For those who have already passed from death to life, it will be a recounting for rewards or lack there of.
And yet it can still seem as though we suffer difficulty in this life because of circumstances and relationships beyond our control. And this seems unfair to us. We understand consequences for our own behavior, but why do hardship and suffering come to us without malfeasance on our part?
In the past, when I've answered this question, even going through explaining using biblical texts, I've found that people desired someone to offer words of comfort rather than words of truth. Words of comfort offer an immediate emotional relief but doesn't last without an undergirding truth that offers freedom and life.
So I'll offer 2 things that have helped me personally:
1. Nothing you are suffering is directly related to another's sin. Believe it or not, the disciples asked this question of Jesus in John 9:1-3 of a blind man. Jesus answer is quite telling. He said what happened was done that the works of God may be manifest in him.
And so it is with us. It's a hard question but one that we all need to answer: can I suffer long and joyfully that God might be made known through me?
When things weren't going as he thought they should, John the Baptist sent disciples to inquire of Jesus. Jesus answer served to refocus John on God and not himself. And Jesus ended with an unusual statement: Blessed is he, whosoever is not offended in me. Jesus was saying we are blessed when we accept the way He chooses to do things. Our response to God's choices for us always reveals our degree of submission to Him.
2. This leads to my second point. It is a surrendered life that is the key to blessing. Matthew 11:28-30 are widely known and little employed verses. We tend to relish in what they offer but seldom truly meet their conditions. Few people get up each day and say to God: here's my life, do as you will. When difficulty comes, we tend to throw off the yolk and fend for ourselves. In doing so, we have little trusted God and missed out on great blessings. How would the story of the 3 Hebrew children in the furnace have turned out if they had done so? Or how about the children of Israel at the Red Sea if they had plunged into the water before God separated it? Or what would life be like if Jesus hadn't gone to the cross but, instead, chosen another course?
There is much more to understand about suffering but I hope as you reflect upon these things, that God will make Himself known to you in a deeper and more intimate way.