The *only* people to get the choice of the half-elven were Earendil, Elwing, Elrond, Elros, Arwen, Elladan, and Elrohir.
Elrond, Arwen, Elladan, and Elrohir were not elves.
Elrond married Celebrian - a full elf. Because of this renewed Elvish strain, their children could choose.
Elros, a mortal, married a mortal. Thus, all their children are mortal, end of story.
Likewise, Arwen, a mortal, married a mortal. Just like Elros' children, hers too were mortal. End of story.
If Elladan and Elrohir were to marry elves, their offspring would get the choice, presumably.
Still confused?
Read this article.