Greetings!
Quickbeam had some excellent points to make! Umbran did as well. As for myself, well, it would seem that there are several angles to approach in the matter.
(1) Killing the Young Hobgoblins
Considering the young Hobgoblins "kids" brings to mind "human kids"--which isn't necessarily equivalent. Morally, there isn't any kind of imperative that would suggest that "Hobgoblin kids" are morally equivalent with "Human kids." It could be seen as a very Good thing to do. In our own day, we don't squirm when "baby rats" or "baby snakes" are killed. We exterminate dangerous creatures to our everyday society without so much as a flicker of hesitation. So it could well be with how people consider Hobgoblins. Whether a particular group of Hobgoblins are old, middle aged, newborn, or somewhere in between is irrelevant. Considering that in the Monster Manual, it mentions that Elves and Hobgoblins are natural and traditional enemies, much akin to the Dwarves and Orcs, it would seem quite natural for the Elf to want to kill them all.
By sparing them, what would he be sparing them for? Even if the alignment in the Monster Manual says "usually evil"--so what? It isn't required that adventurers, and certainly not Chaotic Neutral characters, to enslave their own actions by the thought of what "might be" years down the road. Mathematically speaking, the odds are against the Hobgoblin children growing up to be anything different from vicious, blood-thirsty monsters! So, it makes sense for the Elf character to kill the Hobgoblins--all of the Hobgoblins.
Next, is the issue of "innocence." Innocence of what? By virtue of being Hobgoblins, they are "Guilty." If one thinks that Hobgoblins are "Innocent"--that would suggest that Hobgoblins then go on to commit "crimes" that make them guilty. Crimes according to who, though? Guilty according to who? Hobgoblins don't live their lives worried about what some Elves or Humans think, anyways. In another angle, what makes poisonous spiders or rats "guilty" or "innocent."?
To elaborate--we kill rats and poisonous creatures not because of any supposed guilt, or innocence, but because of what they are, and the threat they pose. "Guilt" or "Innocence" have nothing to do with it. The same thing can be seen to apply with Hobgoblins and other evil humanoids.
(2) Killing The Druid
Well, if the player of the Druid character wants to get mad, let him. All characters who join the group should be expected to help in the fighting. If they don't, it isn't incomprehensible to see why one or more of the other characters would simply kill such excess baggage, and be done with it. A company is a team, that only survives and prospers by everyone working as a part of the team. If one member of the group isn't pulling their weight in sharing in the fighting and the danger, then by that they are posing a threat to the rest of the group and should be killed. Because they aren't doing so--their lack of action, like the Druids'--could lead to one of the other team members being killed. It is absolutely unconscionable for the Druid to remain so cowardly. Instead of him getting mad at the Elf character, or you punishing the Elf character, the whole group should confront the Druid's player, and say if any character he enters the game with doesn't get with the program, then his character will meet a similar fate as the Druid.
In such situations, life and death hangs by a thread. People don't sit there and mull and chew something over all the time. Pose a threat to their survival, and they just kill you quick to put you out of your misery so you don't continue to endanger the rest of the company or the mission by your cowardice. In such close quarters with everyone depending on each other for survival, no character should be allowed to embrace such cowardice without paying the price.
So, it seems that far from being a bad player, it seems that the Elf character is not only playing realistically, but also with some sense of drive and decisiveness. It might also be that the character is attempting to show the rest of the group cool decision making skills, and even leadership for making such difficult command decisions, and in looking out for the long-term welfare of the rest of the group, and the success of their mission.
Leaders often must make the hard moral decisions that make others squirm. Such is the burden of leadership. With such authority and power, comes the burden of making hard decisions that aren't always pleasant, fun, or comfortable. Regardless of how uncomfortable others might be with the situation, the leader must make a decision, and follow through with it's execution. Good, bad, or otherwise.
The Elf's player should be congradulated on such driven and focused play. He sounds like he could be playing a character with conviction, and complex motivation, and multi-faceted personality.
So, let the Elf kill them all. He'll do what needs to be done in a ruthless, vicious world. Let the rest of the party squirm and endlessly debate, attempting in vain to arrive at a "consensus." Meanwhile, the grim Elf marches on decisively, seeking to crush evil, and see the mission through to success.
Semper Fidelis,
SHARK