Mixed Blood

[Aiwendil]

Thus it was only to one mixed line that the Choice was granted, not to all half-elves by blood. Mithrellas was not of the right line.

This was, however, written in the late 1930s, before the characters Elladan, Elrohir, and Arwen existed - so I wouldn't say it's entirely conclusive. Personally, I had always interpreted the "choice" as being inclusive of Elrond's children (though not of Elros's) since the Valar did not have the authority to revoke the Gift of Iluvatar from anyone. However, I have no evidence for this and I'm not sure whether it has some textual basis or not.

I do think, though, that the depiction of the sorrowful parting of Elrond and Arwen in LotR makes more sense if Arwen's choice is understood as a choice for mortality. It always seemed to me that Elrond expected never to see his daughter again.