Brian, If you don't mind I'll give you a bit of history of Tolkien's Aragorn. The following dates are from the calendar used by the Noldor (Elrond and Galadriel) and the Dunedain (Aragorn and the Gondorians). The following dates, quotes, and facts are from the Third Age of Middle-earth and can be found in appendices of The Return of the King. I think all of the following information is pertinent to who Elrond, Aragorn and Arwen are in the story... and I'll throw in a few dates to let you know how Aragorn's life fits into the overall timeline.
2 - Isildur leaves Gondor in the hands of Meneldil, his brother's son, and heads back north to Arnor. He is slain en route along with his three eldest sons. As the elder brother, Isildur considered himself the High King of the Dunedain (the Arnorians and Gondorians).
3 - The shards of Narsil, Elendil's sword that Isildur used to cut the Ring off Sauron's finger, are delivered to Elrond in Rivendell.
10 - Valandil, Isildur's youngest and only surviving son, comes of age and is proclaimed King of Arnor. In the interim, he was called Isildur's heir beginning a tradtional title.
241 - Arwen born.
861 - Feuding brothers divide Arnor into three realms. Arthedain, Cardolan, and Rhudaur. The royal line quickly fails in Rhudaur. Border skirmishes and open war never really ceases between these rival states.
c. 1000 - Saruman, Gandalf, Radagast, and two more Istari (Wizards) first appear in Middle-earth.
1050 - Hobbits begin to migrate into Arnor.
c. 1300 - The leader of the Nazgul (Ringwraiths), the Witch-king, takes up residence near Rhudaur. He establishes the realm of Angmar. Rhudaur quickly succumbs to his influence and becomes a client state. Arthedain and Cardolan cease hostilities and ally themselves against Angmar and Rhudaur.
1409 - Cardolan destroyed.
1432-1447 - Gondorian Civil War.
1601 - Hobbits begin to settle, in large numbers, in an area of Arnor that will become known as The Shire.
1940 - King Arvedui of Arthedain weds Firiel, the daughter of King Ondoher of Gondor.
1944 - King Ondoher of Gondor dies in battle. As his son in law and as the only surviving heir of Isildur (and by extension Elendil), King Arvedui of Arthedain claims the throne of Gondor. General Earnil rallies the Gondorians and wins two overwhelming victories against invaders from the south and east.
1945 - The nobility of Gondor give the crown to Earnil.
1974 - The Witch-king defeats Arvedui and destroys Arthedain.
1975 - The Gondorians (with some help from Elrond's people), under the command of Earnur (Earnil's son), defeat the forces of the Witch-king. The Witch-king abandons Angmar with his mission accomplished. Arvedui drowns in exile.
1976 - Aranarth, son of Arvedui, calls himself Chieftain of the Dunedain and Isildur's heir. His followers are sheltered by Elrond. They range across the north, protecting their former lands from evil.
1980-1981 - The Dwarves of Khazad-dum accidentally awaken a Balrog. It slays two of their kings and they flee. Their kingdom is subsequently infiltrated by orcs and is renamed Moria.
1999 - The Dwarven refugees found a new kingdom at Erebor, the Lonely Mountain.
2002 - Minas Ithil falls to the Witch-king. It becomes the dwelling place for the Nazgul. It is renamed Minas Morgul. (This is the place where Frodo was captured and tortured.)
2043 - Earnur succeeds his father as King of Gondor. The Witch-king sends a message to Earnur claiming cowardice at their previous meeting.
2050 - The Witch-king again invites Earnur to single combat. Earnur accepts, rides forth, and is never seen again. Since Earnur never married, his steward Mardil rules in his name.
c. 2460 - Deagol finds the Ring and is murdered by Smeagol.
2510 - Gondor's norther province is overrun by Easterlings. Easterlings are defeated by Northmen commanded by Eorl. Cirion, Steward of Gondor, gifts the province to Eorl. Eorl calls himself king and names the land Rohan.
c. 2670 - Hobbit's first plant pipe-weed.
2770 - Smaug destroys Erebor and Dale (the town on the lake).
2890 - Bilbo born.
2930 - Denethor born.
2931 - Aragorn, sixteenth in direct descent from Arvedui, born.
2933 - Aragorn's dies. Aragorn is given to Elrond. Elrond raises him as his own son.
2939 - Saruman's spies tell him Sauron's spies are searching the location of Isildur's death. Saruman does not tell Elrond, Galadriel, or Gandalf, aka the White Council, because he wants the Ring for himself.
2941 - Bilbo's adventure. Bard kills Smaug. Battle of the Five Armies. Erebor is re-established.
2944 - Bard re-establishes the Kingdom of Dale.
2948 - Theoden born.
2951 - Sauron openly declares himself as Lord of Mordor. Elrond tells Aragorn of his ancestry and gives him the heirlooms of his house, including the shards of Narsil. Arwen, who had stayed with her grandmother (Galadriel) for many years, returns to Rivendell and meets Aragorn for the first time. Aragorn goes out ranging.
2956 - Aragorn and Gandalf meet for the first time.
2957-2980. Aragorn, using the name Thorongil, spends time serving King Thengel of Rohan (Theoden's father) and then Ecthelion (father of Boromir and Faramir), Steward of Gondor. During Aragorn's time in Gondor, he and Denthor were the two leading captains. Denethor most likely figured out who Aragorn really was.
2968 - Frodo born.
2978 - Boromir born.
2980 - The Corsairs of Umbar take control of the seas from Gondor. Aragorn with a small flotilla enters their harbor at night and burns their fleet. He leaves Gondor for Lothlorien. There he meets Arwen for the second time and they get engaged. Elrond tells Aragorn, "My son, years come when hope will fade, and beyond them little is clear to me. And now a shadow lies between us. Maybe, it had been appointed so, that by my loss the kingship of Men may be restored. Therefore, though I love you, I say to you: Arwen Undomiel shall not diminish her life's grace for less cause. She shall not be the bride of any Man less than the King of both Gondor and Arnor. To me then even our victory can bring only sorrow and parting - but to you hope of hoy for a while. Alas, my son! I fear that to Arwen the Doom of Men may seem hard at the ending."
2982 - Meriadoc (Merry) born.
2983 - Faramir born. Samwise born.
2984 - Denethor becomes Steward of Gondor.
2989 - Balin tries to re-establish Khazad-dum (Moria).
2990 - Peregrin (Pippin) born.
2991 - Eomer born.
2995 - Eowyn born.
c. 3000 - Saruman uses the palantir (the seeing stone) of Orthanc, but is caught by Sauron using the palantir taken from Minas Morgul. Saruman is forced to betray the White Council.
3001 - Bilbo's farewell party.
3018 - The Nazgul enter the Shire. Frodo flees. Council of Elrond.
3019 - Battle of Helm's Deep. Destruction of Isengard. Battle of Pelennor Fields. Destruction of Sauron and the One Ring. Aragorn becomes King of Gondor.
3021 - Bilbo turns 131. Bilbo, Frodo, Gandalf, Elrond, and Galadriel sail away. This is the last year of the Third Age.
1 - Beginning of the Fourth Age.
6 - Sam elected Mayor of the Shire. Aragorn formally incorporates the Shire a part of his re-established Kingdom of Arnor and declares it illegal for any Man to enter the Shire without an invitaion.
11 - Merry becomes Master of Buckland. He is sent lavish gifts from Eomer and Eowyn.
15 - Aragorn visits the Shire.
13 - Pippin becomes Thain of the Shire. Sam is re-elected. Aragorn formally makes the Mayor, the Master, and the Thain Counsellors of Arnor.
48 - Sam wife dies and he retires after serving seven terms. He is last seen riding west and tradition holds that he sailed over the sea.
63 - Merry and Pippin retire. They journey to Rohan and see Eomer before he dies. They then journey to Gondor and live there for a few years until their deaths.
120 - Aragorn laid down and relenquished his life. He is succeeded by his son, Eldarion. He and Arwen also had at least two daughters.
Let me explain a bit about Elrond... from the movie, you get the idea that he hates Men.
Elrond's lineage includes Elves, Men, and an Angel. His bloodline was so convoluted that the Angels gave a choice to him and his twin brother. They could choose to be human or elf. Elrond's brother, Elros, chose to be human. He became the first King of Numenor. When Numenor finally failed after three thousand years, Elendil, the most noble of the Numenoreans left, established two kingdoms in Middle-earth... Arnor and Gondor.
Elrond chose to be an elf. His choice was passed on to his children... as long as he remained in Middle-earth. When he left, his children either had to choose elven and leave with him or stay and be human. All three chose to stay.
Time and time again in the six thousand years since his choice, Elrond assisted the descendants of his brother. By the time Aragorn was born, Elrond had been sheltering Elros' family for a thousand years... talk about relatives that out stay their welcome. He went above and beyond to preserve the heirs of Isildur for three thousand years. He personally adopted Aragorn and raised him as his own son.
Elrond was the product of the greatest heroes of both Elves and Men of the First Age. His ancestors were Melian (an Angel), Thingol (High King of the Teleri, i.e. one of the three branches of the Elves), Luthien (most beloved of Elves), Turgon (High King of the Noldor, another branch of Elves), Idril (a wise princess), and also of Beor, Barahir, Haldad, Marach, Hador, Galdor, Huor, and Tuor... all mighty heroes of the Edain (Men, the forerunners of the Numenoreans).
Elrond could have claimed to the High King of the Noldor or the High King of the Teleri... according to his lineage, he could claim to be King of all the Elves of Middle-earth. He could also claim to be the High King of all three houses of the Edain (Men). But Elrond chose simply to be called the Master of Imladris (Rivendell).
And in the movies, Elrond has to be conviced of the worthiness of both Aragorn and all descendants of Numenor.