The "highborn kinsmen" are Annabel Lee's relatives. We are not told why they disapprove of the speaker's relationship with Annabel Lee, but we can infer that he is from a lower socioeconomic class. After Annabel Lee's death, her relatives take possession of her remains and won't even allow the speaker to attend her funeral.
Some scholars believe this poem is about Poe's love for and marriage to his cousin Virginia Clemm. Their families objected to their relationship not only because they were cousins but also because of the difference in their ages: he was 27 and she was 13!
See the eNote discussion of themes in the poem.
I actually think its referring to God. Thats just a opinion though.