Who can't sympathize with the anguish and moral outrage in this node title? Here is one of the hardest facts of human existence: people die. Even children die, and although we have known this to be a truth about the world nearly all our lives and have known no alternative, we are convinced in our hearts that somehow this is wrong.
Nevertheless, to say that "God has no right to utterly destroy children" is the result of a trap, one that is all to easy to easy to fall into: one starts with an idea of a human being; endows him with one's conception of the highest possible human ethics and the restrictions appropriate to a human being's dealings with other human beings; and then inflates him to enormous size and power, bestowing omnipotence and omniscience, and calls it God.
This god is a construct made up of our wishes and desires, a projection of ourselves and how we would like the Almighty to behave. When He doesn't fit this framework, we become angry and embittered. We may even decide that we are His moral superiors, that we can judge him the way we would (as another contributor to this node suggests) a head of state, the military, or any other earthly power.
God is not a really big human being. He is not a head of state, or the military, or any other human power on which we can sit in judgment:
You turn things upside down,
as if the potter were thought to be like the clay!
Shall what is formed say to him who formed it,
"He did not make me"?
Can the pot say of the potter,
"He knows nothing"?*
We are God's creations. We are clay pots He has made, we are characters in his novel. Any restraint in His dealings with us must by definition grow from His love and mercy, and not from our "rights"; to say otherwise is to imply a power above God that bestows these rights, which leads us full circle because that power would really be God.
So where is His love and mercy in the passage from 2 Kings, where a group of youths who jeer at one of God's prophets are mauled by bears?
Looking at it one way, you have to ask how a supposedly loving and merciful God could destroy anyone. Looking at it another way, you have to ask why a just God doesn't destroy more people. Right now in the city I live in, our attention is riveted on the proceedings of a trial in which a man is accused to kidnapping a little girl from her bedroom, murdering her (perhaps raping her first), and leaving her body to be devoured by animals. Whether the defendant is declared guilty or not, someone did it. If God is going to throw out any of the pots He's made, surely that one must be a prime candidate. He has every right as that person's Creator to take that person out. Whether He does or not is up to Him. For our part, we must seek such justice as can be done in our courts, with a restraint born of a respect for the rights of the accused and his protections under the law.
Now consider the context of the passage: the people of Israel were given a unique revelation of God, were made His people and set apart as a holy nation. Yet 2 Kings 1 shows that things have become very dark. Israel has turned its back on the God of Light and is calling on idols for aid. The king is dispatching troops to arrest any of God's prophets who challenge him. They've sunk so far as a people that when an old holy man arrives at the city of Bethel a gang of youths spots him and hurls abuse at him -- and by extension, at the God that brought them out of slavery to begin with. This is corruption down to that society's very bones. This is evil, and God's absolute holiness will not abide it.
Love in action is a harsh and dreadful thing, compared with love in dreams.
A lot of people get destroyed in 2 Kings.
Were they utterly destroyed? I don't know. I have reason to believe that sooner or later we will all find out.
If you want to, you can take this passage as the final word on God and throw all the rest away in disgust, but it is neither the first nor the last word on the subject. It tells us something about Him that we need to know, but it is not the whole picture. If you want my advice -- and I'm not for a moment suggesting you do -- keep this thing in mind but move on. You may find a light source down the road that will illuminate it.
For a fictional meditation on this kind of destruction and what it means, I recommend C.S. Lewis' That Hideous Strength. Though it's the third in a trilogy, it can stand on its own.