Hello George!
A belated warm welcome to the B.B.
May I ask you if you would advocate prayer for a Christian's unsaved children? It seems to me that such a prayer would be both useless and hypocritical. If I'm reading you right, God seems to have resigned responsibility for anyone's salvation, it's all down to their own free will.
So anyone with unsaved children must do the best he can to convince them of their need of Christ, and if that doesn't work he must look on in helpless sorrow as they wend their way to eternity. His only consolation being that God looks on equally helplessly since He has abdicated all responsibility for salvation as 3 Corinthians makes so clear
Unless he has been up to heaven, had a look at the Book of life and found his child's name missing there, for the believer in Sovereign Grace, it is the sovereignty of God that gives him hope. When all his best arguments and pleading have fallen on stony ground, he does not despair. Maybe tomorrow, maybe next year, God will move in his loved one's heart and bring him to Christ. In the meantime, he besieges heaven with his prayers, knowing that
'The effective, fervent prayer of a righteous man [i.e. someone whom God has justified]
avails much' (James 5:16).
In the parable of the workers in the vineyard (Matthew 20:1-16), some labourers were hired at the start of the day, some at the ninth hour and some at the eleventh. But each one received the same reward. Note also that the labourers could do nothing to hire themselves; they could only wait for the landowner. So it is that some children of believers may resist the Holy Spirit for year after year, but like the Mounties, He always gets His man.