Kirk, after the death of his brother, his sister-in-law and two nephews, with one nephew, Peter, left an orphan.
I recall nothing of his other two nephews dying
That's from the Blish adaptation. In the episode as aired, Peter is his only nephew.
Also, "What are Little Girls Made Of?" has a line of dialogue that gives George Samuel Kirk three sons.
In "Operation: Annihlate!" McCoy says:
MCCOY: Captain, I understand your concern. Your affection for Spock, the fact that your nephew is the last survivor of your brother's family.
http://www.chakoteya.net/StarTrek/29.htm
Clearly McCoy does not know of any other survivors of Kirk's brother's family who went to Deneva.
Does McCoy know that Sam's other 2 sons went to Deneva and that they died, because their bodies were found off screen?
Does McCoy know that Sam's other 2 sons went to Deneva and assume that they died, because theiy have not yet been found, living or dead, where they should be?
Does McCoy know that Sam's other 2 sons didn't go to Deneva, and mean that Peter is the only survivor out the 3 family members who did go to Deneva?
Does McCoy falsely think that Peter was the only child of Sam and not know Sam had 2 other sons who didn't go to Deneva?
Does "What Are LIttle Girls Made of?" happen in an alternate universe where Sam and Aurelan decided to adopt two boys, the other 2 sons, and "Operation: Annihilate!" happen in an alternate universe where they decided not to adopt them?
In canon, there is no proof of any of those.
As for why kirk seems a little odd, ignorning tragedies soon after they happen, perhaps it is PTSD or some other psychological problem.
According to the best guesses of chronologists, Kirk would have been about 13 on Tarsus IV. And although all 4,000 surviving colonists would have known Governor Kodos, and there was a photo of Kodos on file, there were 9 living persons whose testimony would have been necessary to convict Kodos.
LEIGHTON: Jim, Jim, I need your help. There were only eight or nine of us who actually saw Kodos. I was one, you were another. If he's to be exposed,
COMPUTER: Data being received. Kodos file of all survivors. There are nine actual eye witnesses who can identify Kodos
SPOCK: SPOCK: He'd better. There were nine eye witnesses who survived the massacre, who'd actually seen Kodos with their own eyes. Jim Kirk was one of them. With the exception of Riley and Captain Kirk, every other eye witness is dead. And my library computer shows that wherever they were, on Earth, on a colony, or aboard ship, the Karidian Company of Players was somewhere near when they died.
KIRK: You sound certain. I wish I could be. Before I accuse a man of that, I've got to be. I saw him once, twenty years ago. Men change. Memory changes. Look at him now, he's an actor. He can change his appearance. No. Logic is not enough. I've got to feel my way, make absolutely sure.
http://www.chakoteya.net/StarTrek/13.htm
And I wonder whether Kirk saw Governor Kodos only once, or whether he only saw Kodos KIlling his victims once.
It is my belief that all of the people who helped Kodos massacre his victims were killed fighting the relief force which deposed Kodos. And none of persons who Kodos actually killed were alive to testify against him. Only Kirk and 8 other persons, one a boy much younger than Kirk, saw Kodos committ the massacres and survived to tell about it. The history books say Kodos massacred the 4,000 colonists because Kirk and the other 8 witnesses told the relief force they had seen it.
So if the 9 witnesses died before Kodos was found and tried, there would no eyewitness evidence against him. People who only testify that the 9 witnesses had told them that Kodos was in command at the massacre. And that was hearsay evidence, inadmissable in court.
Therefore, Kirk was almost certainly present when Kodos was slaughtering the 4,000 victims. And thus Kirk could have been very traumatized.
And possibly the results of this and other traumas in Kirk's life give him have a different attitude to life and death than normal people have.
I not that Kirk is an experienced commander in space warfare.
In "Whom Gods Destroy":
GARTH: Upon the firmest of foundations, Mister Spock. Enlightened self interest. You, Captain, are second only to me as the finest military commander in the galaxy.
KIRK: That's very flattering. I am primarily an explorer now, Captain Garth.
GARTH: And so have I been. I have charted more new worlds than any man in history.
KIRK: I agree there was a time when war was necessary, and you were our greatest warrior. I studied your victory at Axanar when I was a cadet. In fact it's still required reading at the Academy.
http://www.chakoteya.net/StarTrek/71.htm
So Kirk has a lot of experience in war. And what is war like in Kirk's era?
In "Errand of Mercy"
KIRK: How to handle their interstellar relations! We have the right
AYELBORNE: To wage war, Captain? To kill millions of innocent people? To destroy life on a planetary scale? Is that what you're defending?
KIRK: Well, no one wants war. But there are proper channels. People have a right to handle their own affairs. Eventually, we will have
AYELBORNE: Oh, eventually you will have peace, but only after millions of people have died. It is true that in the future, you and the Klingons will become fast friends. You will work together.
http://www.chakoteya.net/StarTrek/27.htm
In "A Taste of armageddon":
KIRK: I'm not interested in discussing our differences. You don't seem to realise the risk you're taking. We don't make war with computers and herd the casualties into suicide stations. We make the real thing, Councilman. I could destroy this planet.
KIRK: All that it means is that I won't be around for the destruction. You heard me give General Order Twenty Four. That means in two hours the Enterprise will destroy Eminiar Seven.
http://www.chakoteya.net/StarTrek/23.htm
So Kirk could have participated in the destrouction of planets and the killing of millions.
And "Operation: Annihlate!" Couldhave ended much worse than it did.
KIRK: No, no, Bones. There's more than two lives at stake here. I cannot let it spread beyond this colony, even if it means destroying a million people down there.
Captain's log, stardate 3289.8. I am faced with the most difficult decision of my life. Unless we find a way to destroy the creatures without killing their human hosts, my command responsibilities will force me to kill over a million people.
KIRK: I will accept neither of those alternatives, gentlemen. I cannot let this thing expand beyond this planet, nor do I intend to kill a million or more people to stop it. I want another answer. I'm putting you gentlemen on the hot seat with me. I want that third alternative.
So in that epiisode Kirk may be rather happy at the end, despite losing two of his family members,because he has saved another family member, and has also avoided killing over a million people to save billions.
