In the Silmarillion, the judgement of Manwe is that Earendil and Ewing get to Choose between elvenkind and humankind, as do their sons. Now, you can read that as their actual sons, Elros and Elrond, or sons in the more general sense as in progeny - e.g. the Pevensey children are ‘Sons of Adam’ in Narnia. In support of the latter case is that Arwen gets to Choose too, and she’s most definitely not the son of Earendil - she’s his granddaughter. But if that’s the case, don’t the descendants of Elros also get to Choose too? Could Aragorn have Chosen to be judged as Elvenkind?
Nope. The scions of Elros had no choice. This was spelled out to them on more than one occasion, including when the kings of Numenor started to fear death, and questioned why they couldn’t be like their ancestor Earendil, whom was still sailing around in the sky, showing off the Silmaril. At that time, Eldar from the Undying lands came to Numenor as representatives of the Valar, to 'splain it to em.
Is that entirely accurate? The kings of Numenor wanted to be human yet immortal, which is a no-no. Could they have chosen instead to be elven and immortal?
The first one, yes. Maybe even his children. But after that, they were basically human and had no more than a trace, albeit a very handy trace, of elven blood.
No cite, but I do recall reading, either in UT, or more likely in HOMES, a few pages about the gathering of Vala to decide the fates of the Peredhil. There I do believe I recall it stated explicitly that the choice was offered only to Elros and Elrond, but then once Elrond chose to be elven, the choice of whether to remain elven or to become mortal would also be given to his children.
I will look for a cite.
I do hypothesize that it’s easier for an Eldar to opt out of the music and become mortal, with an unknown destiny than it is for a mortal to opt into the music and have his Eru-given special destiny taken away.
And to forstall argument, I don’t believe it’s canon that Tuor became Eldar: IIRC JRRT only wrote that “it was rumored” that Tuor became one of the Eldar.
From The Silmarillion, Chapter 23 (Of Tuor and the Fall of Gondolin):
Just providing textual evidence for your forestalling… 
Well, if they sang it, it might be canon. But only if some of the Ainur sang along…
I feel uneasy here,any minute now you guys are going to start speaking in Klingon aren’t you?
Sindarin, actually.
A Elbereth Gilthoniel
silivren penna miriel
galadhremmin ennorath…
And this is where this wee Elenfair climbs up onto Uncle the Mercotan’s lap, sits, and listens in, fascinated by the wealth of knowledge… and learns somethin’.
I was just reading the Chapter on Eärendil today.
In the AKALLABÊTH Tolkien did not discuss the children of Elrond & Elros. Celebrían, Arwen, Elladan & Elrohir were not even mentioned in the Silmarillion.
Elros had four children: Vardamir Nolimon, Tindomiel, Manwendil and Atanalcar.
No mention was ever made of them having a choice, but they all died so it is safe to assume that either they had no choice or chose to be mortal.
BTW: Tolkien never actually said what Elladan and Elrohir chose. He merely said they were not yet weary of Middle Earth.
You know, threads like these are just one reason why I love the SDMB.