Would Arwen's children get a choice between mortality and immortality?

[Legolas]

Ah ha!

This is why Elladan, Elrohir, and Arwen get the choice: their mother is Elvish.

Letter No. 153:

The view is that the Half-elven have a power of (irrevocable) choice, which may be delayed but not permanently, which kin's fate they will share. Elros chose to be a King and 'longaevus' but mortal, so all his descendants are mortal, and of a specially noble race, but with dwindling longevity: so Aragorn (who, however, has a greater life-span than his contemporaries, double, though not the original Númenórean treble, that of Men). Elrond chose to be among the Elves. His children - with a renewed Elvish strain, since their mother was Celebrían dtr. of Galadriel - have to make their choices.

Arwen chose mortality and wed a mortal, thus their children would not have the choice. Elladan and Elrohir are in a different situation - if they chose to share elven fate and wed elven maidens, I imagine their children too would have the choice.