Only one lineage?

[Tar Elenion]

Now that just doesn't make sense. Why should a reinfusion of Elvish blood make it necessary for Elrond's children to choose? Why shouldn't it just confirm their Elvish identity as their cousin's Mortal blood on their mother's side supposedly confirmed theirs as Men?

Did the 'reinfusion' make it "necessary" for them to choose? Or was that simply a reason Manwe used to grant them 'other doom'.

Thank you for reminding me of the 'same potential for life' quote, IMO it furnishes confirmation for my theory by indicating that the Half-Elven inherit the immortality of their Elven parent but the Gift of Men from their Mortal. I wonder, is Elrond completely free of the 'seeking elsewhere' trait? How content is he going to be in changeless Aman, how content are Elwing and Earendil?

They inherit a 'potential', but they are not 'immortal' (and remember the essential difference between Elves and Men is not how long they live, but what happens after they die) unless granted that by Manwe. As Manwe said: "Now all those who have the blood of mortal Men, in whatever part, great or small, are mortal, unless other doom be granted to them...". All Half-elves are by nature mortal.

One can't help but notice that the majority of the Half-Elven choose Mortality; Elros, his children, Arwen and the Twins - do they maybe know something we don't?

The Half-elves who were granted a Choice: Earendil, Elwing, Elrond, Elros, Elladan, Elrohir and Arwen.
Earendil, Elwing and Elrond all chose 'immortality'.
Elros and Arwen Chose 'Mortality'.
We do not know what Elladan and Elrohir Chose, the most specific statement JRRT wrote about them is: "Elrond passes Over Sea. The end of his sons, Elladan and Elrohir, is not told: they delay their choice, and remain for a while."
Letter 153
Elros' children did not Choose mortality. Elros' children had no Choice. They were 'mortal':
"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..."
Letter 153
JRRT is quite specific.