“Can you show me a Calvinistic Confession that categorically states that God elects or has elected all children who die before a certain age?”
It doesn’t.
Westminster Confession - Chapter 2: Of God, and of the Holy Trinity
2. God has all life, glory,[ goodness, blessedness, in and of Himself; and is alone in and unto Himself all-sufficient, not standing in need of any creatures which He has made, nor deriving any glory from them, but only manifesting His own glory in, by, unto, and upon them. He is the alone fountain of all being, of whom, through whom, and to whom are all things; and has most sovereign dominion over them, to do by them, for them, or upon them whatsoever Himself pleases In His sight all things are open and manifest, His knowledge is infinite, infallible, and independent upon the creature, so as nothing is to Him contingent, or uncertain. He is most holy in all His counsels, in all His works, and in all His commands. To Him is due from angels and men, and every other creature, whatsoever worship, service, or obedience He is pleased to require of them.
Westminster Confession - Chapter 3: Of God’s Eternal Decree
1. God from all eternity, did, by the most wise and holy counsel of His own will, freely, and unchangeably ordain whatsoever comes to pass; yet so, as thereby neither is God the author of sin, nor is violence offered to the will of the creatures; nor is the liberty or contingency of second causes taken away, but rather established.
2. Although God knows whatsoever may or can come to pass upon all supposed conditions; yet has He not decreed anything because He foresaw it as future, or as that which would come to pass upon such conditions.
Westminster Confession - Chapter 5: Of Providence
1. God the great Creator of all things does uphold, direct, dispose, and govern all creatures, actions, and things, from the greatest even to the least, by His most wise and holy providence, according to His infallible foreknowledge, and the free and immutable counsel of His own will, to the praise of the glory of His wisdom, power, justice, goodness, and mercy.
2. Although, in relation to the foreknowledge and decree of God, the first Cause, all things come to pass immutably, and infallibly; yet, by the same providence, He orders them to fall out, according to the nature of second causes, either necessarily, freely, or contingently.
If we take as a starting point that all sinned in Adam and judgment and condemnation came upon all men because of Adam’s sin and our sinning in him, then all men are under condemnation including the unborn and under-aged persons. Men are under condemnation, not because of their sins, but because of the imputed sin of their natural federal head, Adam. Now if we take into account God’s omniscience “Although God knows whatsoever may or can come to pass upon all supposed conditions” then God knows not only what will actually come to pass (one trusts to salvation) but also, in the case of the unborn or the under-aged child, what would come to pass (that some would trust to salvation) had they been born or lived. Rev. 17:8 says that the names were written in the book of life from the foundation of the world, so God knows those that are His from the foundation of the world. That is the peace that God gave K and me when we lost our first child; God knows those that are His.
Which is why it is quite understandable that people recoil at the idea of Calvinism. Calvinism, when taken at its core, is exactly the polar opposite of the idea that any man can be assured of his salvation, no matter what kind of life he leads, or what his outward spiritual life has been or what decisions he has made. In the Calvinistic world how a man lives his life is ultimately irrelevant to his standing before God. If he is elect, then he is elect and nothing he or she does in this life can change that. If a man is not elect, then nothing he or she does in this life can change that. Therefore no man can state that he is saved, nor can anyone pass judgment on whether or not some person, be they an infant or an old man, is headed for eternal reward or eternal punishment.
If you reject the formula that "all those who call upon the name of the Lord shall be saved," then there is no assurance of Salvation. While it is clearly an axiom that we are all at the mercy of the Lord, what promise can you point to in the Calvinist theology wherein you can be assured of your salvation? How can we be assured that we are under God's mercy if he has no conditions upon which he gives mercy?