My original interpretation was:
1st kid dies in battle
2nd kid dies in childbirth
Although this doesn’t make as much sense as some of the other suggestions - I agree with you it would be hard to write an OP that is less clear - but still kinda draws a picture in your mind 
Chinese:
战死 - zhànsǐ - to die in battle, death in battle
Japanese:
戦死 - senshi - to die in battle, death in battle
It’s essentially the same word. I can’t, off the top of my head, think of a single word to mean to die in childbirth. Make of that what you will.
Generally, “dying in childbirth” means the mother dying. The child dying is “dying at birth”.
In French, a baby who dies while being born is called “mort-né” (literally “dead-born”). To my knowledge, there is no single word for dying in battle; we say “mort au combat” (“dead in battle”) or “tombé au combat” (“fallen in battle”).
I think that the Swedish verb “stupa” originally meant “to die in battle”.
ETA: It is certainly one of its meanings, even today, though not the only one.
Hello again…
2nd event:
A woman who dies in the act or hard upon giving birth. Don’t give a damn about the kid.
::retreats avoiding thrown vegetables::
Also, always listen to the walrus.
Also, Johnny, hit us with some Latin…
Your question is still unclear.
Are you looking for one word that fits both situations or a different word for each?
And 1) Are you looking for “To kill another in battle” or “To die in battle”?
And is 2) A verb “To die giving birth” or the noun form of a woman who suffers this?
what? /lobs a tomato
i think the OP is a relevant example of why sometimes, there shouldn’t be a single word to express a sentence.
Doesn’t have to die *while *being delivered - any baby dead on arrival, for any reason, is mort-né (stillborn). Some do die during delivery, but more commonly the baby dies in utero for one reason or another and has to be delivered anyway.
Mortalparturition.
Also stillborn.
So no word in English to cover the mother, but one for the child.
Mmm, I wonder if Mayan has a word that means both? People who die in battle and mothers who die in childbirth were part of the special class that got to go direct to heaven in Mayan mythology, and I wonder if there was a special word for that?
ETA; I see the Aztecs, at least, had a name for the mothers’ spirits in Nahuatl.
Yeah, I first thought the OP was looking for a word that meant both die/dead in battle and die/dead in childbirth. Lumping together both fallen warriors and fallen mothers in the same, presumably highly revered, category.
Rand el’Torr’s mother died while giving birth to him AND at the same exact time fighting in a war. Is that what the OP means? Falling in battle whilst giving birth.
No, that’s not what the OP means.
Re-read the thread.
If only there was a series of words that accurately described the question the OP is asking. Alas, the OP hath not found it.
Or even just one word.
Or two. Or something.
In German, you could say “Schlachtentod” for death in a battle of war, and “Kindsbetttod” for death of the mother in childbirth. Both words are rare, the first mostly used poetically,
Which makes me think about collocations, and I think French has one in common in English actually : you can die, croak, perish, kick the bucket, keel over, “leave”, go to a better place, buy the farm, lose your life or pass on just about anywhere ; but you only ever “fall” in battle, don’t you ?
OK, that was funny.
Seriously, Leo, would it kill you to write a clearer OP?