Why should our children be with us in worship? They belong to the covenant of grace.
Our children belonging to the covenant of grace and receiving the blessings of it is like belonging to a family. As members of a family, everyone from the oldest to the youngest receives the blessings of the family such as love, shelter, and guidance. We do not regard our children as outside our family any more than we should regard them as outside God’s family, the church. As one writer stated, why would the Apostle Paul go out of his way to address the children of the congregations of Ephesus [Eph 6:1-4] and Colossae [Col. 3:20] if they were not part of the covenant of grace?
This is from the excellent little book, The Nursery of the Holy Spirit.