Walaykum Salam Sister Ruhi.
Good you came by. It reminds me to put up some information on this topic which I should have some months back but forgot. I found a good commentary which seems the most acceptable, but of course only Allah knows best.
It's very likely that the reference is neither to first 10 nights of Hajj nor last 10 of Ramadan. It's simply a description of the passing of the 30 days of every month. This commentary is from Abu Alaa Maududi, quoted below:
On "ten nights" .......
QUOTE -
"By the ten nights." If the context is kept in view, it will become plain that it implies each group of the ten nights among the thirty nights of the month, the first ten nights being those during which the crescent moon starting as a thin nail. goes on waxing every night until its major portion becomes bright; the second group of the ten nights being those during which the greater part of the night remains illumined by the moon, and the last ten nights being those during which the moon goes on waning and the nights becoming more and more dark until by the end of the month the whole night becomes absolutely dark."
UNQUOTE -
On "even and the odd" ..........
QUOTE -
"Even is the number which is divisible into two equal parts, as 2, 4, 6, 8, and the odd the number which is not so divisible, as l, 3, 5, 7 .... Since the context here concerns the day and the night, the even and the odd mean the alternation of day and night in the sense that the dates of the month go on changing from the first to the second, and from second to the third, and every change brings with it a new state."
UNQUOTE -
I repeat, this one sounds most acceptable to me. There have been more than 2 dozen tafsirs by different clerics and jurists on these two Verses, but none have thought of this point. All of them talk about first 10 Hajj nights and some refer to last Ramadan nights .. all in connection with traditionalist information but no one focusing on the Quran independently. Maududi is the first one who has explained it without being hung up on traditions, at least not this time.
I am of the opinion that you explain this commentary to your kids. And simply inform them that mainstream traditionalists pick of Hajj or Ramadan nights but without evidence; so that if they watch or hear the lectures of jurists referring to the usual traditions, the children won't get confused. But let them know that Maududi's explanation is most likely the right one.
Btw .... SubhanAllah, we have completed a decade running MV !!!! Allah is the Greatest!
FOR MORE DETAILED INFORMATION ON THIS TOPIC, PLEASE ALSO READ OUR POST ON HAJJ (click link).