Oh, it's quite Biblically sound.
See the line I've emboldened. That line says it all. God is patient with us. God searches for us until God finds us. We are also told that We do not choose God -- but God chooses us.
All people are not God's children??? Didn't God create us all? Did God not give each one of us a soul? Did not God breathe into each of us God's Spirit? Your model presents a God who is very conditional -- not at all the God presented by Jesus.
God is patient with us, true. The Bible says if WE search for God with all our heart we will find him. If WE humble ourselves, (resist the Devil and he will flee from us) and draw near to God, God will draw near to us. It says God will not always strive with us. God chose all of us to be saved but gave us freewill. You said God is not weak and helpless to watch men he created go to Hell. But everyday we see men (ourselves, too) sin and rebel and turn from God. This does not make him weak and powerless over sin, it just means he gives us a choice--life or death. Just as he is not weak and powerless just because men openly rebel against him all their lives, he cannot be considered so because men choose death. Because he did not make us 'robots' we have a choice to make, and sadly, many choose rebellion and pride and selfishness and reject God's love and gift of salvation.
As far as being God's children, I understand what you mean, God created Adam and Eve and they procreated us and God loves all of us. However, the BIble does distinguish between Children of Light and Children of Darkness. When we have accepted the free gift of salvation we are translated into the Kingdom of Light, and adopted into God's family as sons and daughters of God. However before that, the Bible calls us children of wrath, children of disobedience, and children of darkness. It tells us that we were such but are now children of God. (I think I have shared that with all the verses before) I did a word search on "the wicked" the other day. Hmm, let me paste a few verses:
Job 21:30
That
the wicked is reserved to the day of destruction? they shall be brought forth to
the day of wrath.
Job 31:3
Is not
destruction to the wicked? and a strange
punishment to the workers of iniquity?
Psalm 7:11
God judgeth the righteous, and
God is angry with the wicked every day.
Psalm 9:17
The wicked shall be turned into hell, and all the nations that forget God.
Psalm 11:6
Upon the wicked he shall rain snares, fire and brimstone, and an horrible tempest: this shall be the portion of their cup.
Psalm 36:1
The transgression of
the wicked saith within my heart, that
there is no fear of God before his eyes.
Psalm 119:155
Salvation is far from the wicked: for they seek not thy statutes.
Proverbs 10:30
The righteous shall never be removed: but
the wicked shall not inhabit the earth.
(the righteous shall inherit the earth, perhaps the New Earth of eternity future?)
Isaiah 3:11
Woe unto the wicked! it shall be ill with him: for the reward of his hands shall be given him.
Isaiah 13:11
And
I will punish the world for their evil, and
the wicked for their iniquity
Isaiah 48:22
There is no peace, saith the LORD, unto
the wicked.
Matthew 13:49-50
So shall it be at the end of the world: the angels shall come forth,
and sever the wicked from among the just, 50And shall cast them into the furnace of fire: there shall be wailing and gnashing of teeth.
Okay, well there are hundreds more, but that is enough. Suffice it to say as terrible as eternal punishment sounds, it IS throughout the Bible. We cannot ignore it no matter how nice a theory we develop:
Matthew 25:46
"Then they will go away to
eternal punishment, but the righteous to
eternal life."
Jude 1:7
In a similar way, Sodom and Gomorrah and the surrounding towns gave themselves up to
sexual immorality and perversion. They serve as an example of those
who suffer the punishment of eternal fire.
Isaiah 33:14
The
sinners in Zion
are terrified; trembling grips the godless: "Who of us can dwell with the consuming fire? Who of us can dwell with everlasting burning?"
Jeremiah 23:40
I will bring upon you
everlasting disgrace—everlasting shame that will not be forgotten." (doom of false prophets)
Daniel 12:2
Multitudes who sleep in the dust of the earth will awake: some to
everlasting life,
others to shame and everlasting contempt.
2 Thessalonians 1:9
They will be punished with
everlasting destruction and
shut out from the presence of the Lord and from the majesty of his power
Jude 1:13
Raging waves of the sea, foaming out their own shame; wandering stars,
to whom is reserved the blackness of darkness for ever.
Mathew 13
37He answered and said unto them, He that soweth the good seed is the Son of man;
38The field is the world; the good seed are the children of the kingdom; but the tares are the children of the wicked one;
39The enemy that sowed them is the devil; the harvest is the end of the world; and the reapers are the angels.
40As therefore the tares are gathered and burned in the fire; so shall it be in the end of this world.
41The Son of man shall send forth his angels, and
they shall gather out of his kingdom all things that offend, and them which do iniquity;
42And shall cast them into a furnace of fire: there shall be wailing and gnashing of teeth. 43Then shall the righteous shine forth as the sun in the kingdom of their Father. Who hath ears to hear, let him hear.
Mathew 25
31When the Son of man shall come in his glory, and all the holy angels with him, then shall he sit upon the throne of his glory:
32And before him shall be gathered all nations: and he shall separate them one from another, as a shepherd divideth his sheep from the goats:
33And he shall set the sheep on his right hand, but the goats on the left.
34Then shall the King say unto them on his right hand, Come, ye blessed of my Father, inherit the kingdom prepared for you from the foundation of the world:
41Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels: 46And these shall go away into everlasting punishment: but the righteous into life eternal.
Revelation 20:15
And whosoever was not found written in the book of life was cast into the lake of fire.
Revelation 21:8
But the fearful, and unbelieving, and the abominable, and murderers, and whoremongers, and sorcerers, and idolaters, and all liars, shall have their part in the lake which burneth with fire and brimstone: which is the second death.