I read your question: What happens to children when they die?
You said that David would see his child when he died. I don't understand this because Acts 2:34 says that David has not ascended into the heavens. (David was long dead by this time). Also, John 3:13 says no one has ascended into heaven except Christ. Also, John 5:28 says that all are in the graves and that they will hear His voice and come forth.
It seems from all these scriptures and many more, that Christ will return to the Mount of Olives (and the mount shall split in two Zechariah 14:4) and those waiting in the graves will hear the Trumpet (I Cor 15) and be raised from the grave.
I read the Bible a lot and have found this to be a question. I guess my question is: Don't you believe in the Resurrection? Revelation 20 talks about the Resurrections too.
I believe the confusion comes about because death is a two-step journey. See When you die, do you go straight to heaven or hell? for details. God says that after death we enter the realm of the dead, which is called the grave (Sheol in the Hebrew and Hades in the Greek).
David said, "But now he has died; why should I fast? Can I bring him back again? I will go to him, but he will not return to me" (II Samuel 12:23). David could join his child in the grave, and eventually in Heaven after the Judgment, but now that the child has died, the child cannot return to David.
At the time Peter spoke David was still in the grave, "For David did not ascend into the heavens, but he says himself: 'The LORD said to my Lord, "Sit at My right hand, till I make Your enemies Your footstool"" (Acts 2:34-35). The resurrection had not yet taken place. The same is true of Jesus' statement: "No one has ascended into heaven, but He who descended from heaven: the Son of Man" (John 3:13). Only Jesus, who left heaven, is able to return to heaven after his death. "Seeing then that we have a great High Priest who has passed through the heavens, Jesus the Son of God, let us hold fast our confession" (Hebrews 4:14). So, yes, those who have died are still in the graves awaiting the call. "Do not marvel at this; for the hour is coming in which all who are in the graves will hear His voice nd come forth -- those who have done good, to the resurrection of life, and those who have done evil, to the resurrection of condemnation" (John 5:28-29).
How you conclude that I might not believe in the resurrection from David saying he would join his child after death is something I cannot figure out.
"Behold, I tell you a mystery: We shall not all sleep, but we shall all be changed -- in a moment, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, and the dead will be raised incorruptible, and we shall be changed. For this corruptible must put on incorruption, and this mortal must put on immortality. So when this corruptible has put on incorruption, and this mortal has put on immortality, then shall be brought to pass the saying that is written: "Death is swallowed up in victory"" (I Corinthians 15:51-54).