So in reading all this, could it be the point of decision for the children of Elrond was at the point Elrond himself leaves Middle Earth? If this is the case, then even though Arwen 'chose' to give up the choice before-hand and remain with and marry Aragorn, the decision didn't become solid until Elrond left. Since I believe Elrohir and Elladan remained in Moddle Earth as well, they had no further choice in their fate.
Of course, maybe Aragorn, realizing he was aged and likely sensed that he was beginning to lose his mental abilities (forgetfulness as an early onset of Alzheimer's?), decided wanted to pass the Kingship to Eldarion and lay down his life before he got worse.
Annalist, Physician, & Historian
of The Black Company of the Dúnedain,
The Free Company of Arnor