dchernik, I do not think I will have a productive conversation with, and that is fine.
But, for the rest of you, since it is an interesting question, and I did not explain myself well, dchernik is correct that Samuel gets mad at the Israelites’ failure to follow the Lords command here.
However, the part Samuel and God get mad at them for, is LOOTING. God wants them to forgo looting, not to be nice, but to prove that they are doing it for him and not for their own profit. He is mad that they took cattle and sheep and took the valuable hostage, the king, as prisoner.
When Samuel partially corrects this error by killing the king, he says he does it, because of stuff the KING HIMSELF IS PERSONALLY GUILTY OF.
Samuel does not get mad, nor can I think of any place in the Bible where God gets mad, because a human does not kill a baby. In fact, he says that even the Canaanites killing Canaanite babies gets him mad. I can, however, think of plenty of times where God gets mad for looting after a battle.
Which is why I think that “Kill the livestock!“ Is more literal than “Kill the noncombatants!“ But even here, I think what Samuel meant was not “Kill the livestock! Even if, like a donkey starts running away, and the donkey is like far, and you would have to go on a big campaign to kill it through enemy territory, you just, you really gotta be meticulous about killing it.“
Not because that would be immoral (cause I really do not care about how livestock feel), just because it would be weird, and not make sense. What would be the point? The Israelites weren’t gonna steal it and the Amalekites were not using it anymore. The point of the command is relevant in interpreting it.
The same attitude is how I look at the command to kill the children. Just, why? So, I think it fits with the noncontroversially many many times that one sees hyperbole in war literature from the ancient near East, and in specifically the Bible. Which is so common, it got the title “Semitic hyperbole.“
I know that answer may not be as cool and Kierkegaardian as some answers, and not as appealling as the academic neoMarcion answer, but I think it difficult to get away from its possibility.