You know, I should point out that Legends was merely establishing the orgin story of Dracula versus the Belmont Clan and not the family's history. Hell, even Lament didn't do that. The Japanese storyline, unlike the American, one never claimed that she was the actual first only the first Belmont warrior who was a dudette. Dracula's orgin was already explained in Castlevania III (the manual of Akumajou Densetsu) and Symphony of the night, so in that aspect the game didn't really fell short since there was nothing that needed any more explaining, though some kind off recap would have been nice.
And that all the Belmonts are now Quarter Vampires.
Even if Trevor would have had vampiric blood he is still a Belmont, the only ones who can carry the whip without consequences. He would be its rightful wielder and enemy at the same time. It can't be said how the whip would react since it comes down what the story writers make of it if something like that would ever occur, not your own personal view on the situation.
Don't get me wrong here, I hate SoniaxAlucard and the whole thing is deemed impossible by Castlevania Judgment but it was merely hinted upon so whatever. Not that this all really matters since Legends is an AU story according to IGA. I kind off like that idea.