I am going to go about this in a roundabout way but I promise the end will feature a solid answer.
There are 3 instances of the fates of the Children of Ilúvatar changing. The first two are different than the last.
The first is after Beren and Lúthien are returned to Middle-earth after capturing the Silmaril and they dwell on Tol Galen. Lúthien chooses to become mortal and go where Beren goes after death. (Timeline note: After they die the Silmaril is brought to Dior.)
The second is less certain and deals with Tuor. As he was aging towards death he decided to sail into the West with Idril. Officially, they are never heard from again in Middle-earth. According to Tolkien (Letter 153) it’s only conjecture that his fate was joined with the Firstborn.
The third is after Eärendil, breaking through the ban with the power of the Silmaril on his brow, visits the Valar and pleads for them to save Middle-earth. At this point Eärendil, Elwing, Elros and Elrond are allowed to choose for themselves which kindred they are to be joined. The ability to choose their kindred was a decision of Manwë, who was allowed discretion on the matter by Ilúvatar himself. Here is the quote from The Silmarillion:
But when all was spoken, Manwë gave judgement, and he said: 'In this matter the power of doom is given to me. The peril that he ventured for love of the Two Kindreds shall not fall upon Eärendil, nor shall it fall upon Elwing his wife, who entered into peril for love of him; but they shall not walk again ever among Elves or Men in the Outer Lands. And this is my decree concerning them: to Eärendil and to Elwing, and to their sons, shall be given leave each to choose freely to which kindred their fates shall be joined, and under which kindred they shall be judged.'
Now to return to the matter of Dior at some point in this sequence of events after Dior received the Silmaril he was killed attempting to defend the realm of Doriath, and his two sons Elured and Elurin were left to starve in the forest. After that Elwing took the Silmaril with her down to the Mouths of Sirion where eventually she flew it out to Eärendil's ship and they continued on to Valinor.
If you stop at the published version of The Silmarillion, that's all the information there is. He died before Manwë gave the choice to the other half-elven, and nothing is said of his fate after his death. However in an earlier version of The Silmarillion, published in The Lost Road and Other Writings, Manwë says something a little different before his decree:
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; but in this matter the power of doom is given to me. This is my decree: To Eärendel and to Elwing and to their sons shall be given leave each to choose freely under which kindred they shall be judged.
That's pretty definitive and it squarely places Dior and his children among mortal Men before the decree of Manwë which allowed choosing.
That's the best extant, text-supported answer I could find.
Personally I feel, given more time that Tolkien would have found a more satisfying simpler answer for this question had he been able to further revise his work.