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Since I believe that Christ died to pay for my sins in full, and thus since I believe my name was written in the Book of Life from before the foundation of the world, and since I believe it is God who gives children to parents, then I can be reasonably assurred that my children are part of His family, too. God creates families. He created my family to love and obey Him.

And by His will, we do.

You seem incredulous that anyone would presume their children are among God's family. Scripture tells parents to believe exactly that...

"She is not afraid of the snow for her household: for all her household are clothed with scarlet." -- Proverbs 31:21

"He will bless them that fear the LORD, both small and great.
The LORD shall increase you more and more, you and your children." -- Psalm 115:13-14

"For the promise is unto you, and to your children, and to all that are afar off, even as many as the LORD our God shall call." -- Acts 2:39

"And again, I will put my trust in him. And again, Behold I and the children which God hath given me." -- Hebrews 2:13