"years residents of this State. In early life they became earnest and devoted members of the Methodist Episcopal Church. In that church they held prominent connection, and labored for the conversion of sinners, and to build up the cause of God, for a period of forty years. During this time they had the joy of seeing their children, eight in number, all converted and gathered into the fold of Christ. LS 17.1"
"Lo, children are an heritage of the Lord: and the fruit of the womb is his reward."
The EGW passage mentions the joy of parents seeing their children converted, while Psalm 127:3 states that children are a heritage from the Lord. The connection is the idea of children being a blessing and a source of joy, especially in a religious context.
"And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house."
The EGW passage describes parents working for the conversion of sinners and seeing their children converted, while Acts 16:31 contains the promise of salvation for a household. The connection is the idea of family members being converted and saved.