I have posted a question about the translation of μισέω in Romans 9:15, which quotes Malachi 1:2-3. To further dig into the question of whether "rejected" is a correct translation, I would like to know: Do we have textual evidence from other passages within the Old Testament or other Hebrew writings that would countenance the understanding of שָׂנֵא as meaning "rejected" in this text? Further comments on the interpretation of the Hebrew of Malachi 1:2-3 are welcome as well since my Hebrew does not extend much beyond a few dozen basic vocab words.
In Brown, Driver, Briggs Lexicon, they list the meanings of sone and its permutations as "hate, hatred, abhor, detest, foe, etc." They also note that it can be used in some cases for "revulsion/repulsed." The examples they give are 2 Sam 13:15, Dt 22:13, 16; and 24:3.
In the Deuteronomy verses, we see that she is being turned away and divorced. In that sense she is rejected.
R L Harris also says this in the Theological Wordbook of the Old Testament.
Harris was the general editor of the work and added this paragraph to the entry on sone written by another scholar, G. V. G.
שנא always includes the meaning of rejection in the OT, but never loses its primary meaning of "hate". See Genesis 37:4, where "love" and "hate" contrast in the same verse about Joseph and his brothers.
There is no OT word for "rejection" in the sense that we use the word. The closest is עזב (azav), meaning to leave something, as in אישה עזובה a woman whose husband has left her (though not necessarily hated) often used allegorically to describe the relationship between the people of Israel and the Almighty.
Another similar word is יטש (yatash) meaning to abandon as in 1 Samuel 12:22, and Psalm 94:14. The latter verse uses both yatash first and then azav in classic Biblical parallelism.
The translation "turned against her" in Dt 22 and 24 is a daintiness for the Western ear. The simple meaning is hate, and in the case of Dt 22, the husband is not allowed to reject the wife, at least in the legal sense, although he hates her.