Robert,
     You forgot to mention 1Cr. 7:14. "For the unbelieving husband is sanctified by the wife, and the unbelieving wife is sanctified by the husband; otherwise your children would be unclean, but now they are holy." Why would Paul even mention this unless children of two unbelieving parents resulted in unholy children. Also Rev 3:5 says " He who overcomes shall be clothed in white garments, and I will not blot out his name from the Book of Life; but I will confess his name before My Father and before His angels." There are actually 8 verses in the bible that mention the "book of life". All the infants and children who have died that did not have at least one believing parent will not be raised until the White Thrown judgement. There they will be judged by there works, and since they did not have any works but neither did they reject Jesus, there names would not have been blotted out, and they will be allowed access to the new heaven and earth. A lot of people get caught up in wondering whether children and animals go to heaven, and I usually avoid reading those posts. Phil. 2:12,13 says "Therefore, my beloved, as you have always obeyed, not as in my presence only, but now much more in my absence, work out your own salvation with fear and trembling; for it is God who works in you both to will and to do for His good pleasure." Please look at the fruit your life is producing. The time is so short.
 
Jason Robillard