2 Samuel 7:19
“And as if this was a small thing in Your eyes, O Lord GOD, You have also spoken about the future of the house of Your servant. Is this Your custom with man, O Lord GOD?”
God rewards faithfulness. When we accept Him this affects our family. In Acts 16:31 when one asked how to be saved, this was the response, 'They replied, “Believe in the Lord Jesus and you will be saved, you and your household.”' His love spreads to those in our house. While I don't believe it's literally all, we pray for them and God reaches out to them.
God says in Exodus 20:6, "but showing loving devotion to a thousand generations of those who love Me and keep My commandments." When we follow the Lord He blesses us and our house and future generations. I don't think this means none will ever go astray, but He will keep many.
The Lord protects His children. Jesus says in John 10:28, "I give them eternal life, and they will never perish. No one can snatch them out of My hand." Our children must accept Christ on their own. However, their parents pray for them, they've been raised in The Way, scripture has been taught them. While they must accept Christ, they have many advantages and protections. The chances are good that they will accept Christ.
Along those same lines Proverbs 22:7 says, "Train up a child in the way he should go, and when he is old he will not depart from it." This is a strong, general principle. Most kids will stay in the lane that their parents gave them. They can stray, but they often return. The same is true for those raised in the faith. Even more so, as they've been raised in the Lord and His power is around them. Their parents have dedicated them to God and they've been surrounded in prayer.
Lord, thank You that You keep that which have been committed to You.