"Thus, it seems that Aragorn had to choose between two distant cousins."
Not really. There was never any suggestion of a 'choice' that Aragorn had to take, of Arwen over Eowyn. Eowyn loved Aragorn, but there was no question of him 'choosing' her. At any rate, he was already betrothed to Arwen long before.
Actually, though, I don't think they were related. Unless you are sure, of course. King Vidugavia's daughter, marrying Valacar of Gondor, was involved in the bloodline of the South-Kingdom; however Aragorn is wholly of the Northern line. There was no Northman blood in the ancestry of Aragorn to my knowledge.
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