Question

[Inoldonil]

Elrond and Elros (Pereldar, or Halfelves) were both given the choice of which kindred (Men or Elves) they would belong to, because Earendil their father was a Half-elf, his parents being Tuor and Idril, and so too was their mother Elwing, whose father was Dior, son of Beren and Luthien (the latter herself being half elf, half maia in a sense), and whose mother was Nimloth, an Elf of Doriath descended (in one genealogy) from Thingol's brother.

So Elrond and Elros were Halfelves, and were given the choice. Elros chose the fate of Men, and Elrond chose that of Elves. Elrond wedded Celebrian (Galadriel's daughter), and their children were also given the choice. Elros's were not.

Why was Elrond's children given the choice of fate, but not the chilren of Elros?

[Grand Admiral Reese]

Don't know. Maybe it was because one day Elrond and his children were going to have to move to Aman, and they had to have the choice(as having mortal blood is not allowed in Aman except under VERY unusual circumstances). Elros, having chosen the Gift of Men as his fate would never go to Eressea or Valinor. Thus, his children wouldn't be allowed to choose. Or I could be wrong entirely.