"How could God send His own children to hell?"
God does not send His own children to hell. Rather, the children of the devil go to be with their father when they die, and the children of God go to be with their Father.
The assumption that everyone is a child of God is false. Though all are part of the creation of God, not all are children of God. Some are "children of the devil". Jesus said to religious hypocrites that they were just like their "father the devil" (John 8:42-44). Paul said to a sorcerer "you son of the devil" (Acts 13:10).
The popular and modern belief that everyone is God's child flies in the face of the gospel itself. The gospel is that "through faith in Jesus Christ" we have been granted "the right to become children of God" (John 1:12); that if we are led by the Spirit of God then we are sons of God; that we have "received the Spirit of adoption" to the family of God. But until someone is "born again" into God's family, they are in the family of the devil.
There is a way to tell whose child you are. The bible tells us that the answer is manifest by what we do; if we do not practice righteousness we are not righteous, if we do not love we are not Christians. If we sin, meaning continue in sin, we are of the devil, and we know that "the wrath of God is coming upon the sons of disobedience."
The greatest opportunity God has given fallen man is to be reconciled back to Him through Jesus Christ. We all have the opportunity to become children of God if we turn away from our sin, and turn to Jesus Christ.
Scriptures: 1 John 3:10, John 8:44, Galatians 3:26, John 1:12, Romans 8:15, John 3:3, 1 John 3:10, 1 John 3:8, Ephesians 5:6, Colossians 3:6