From what I can tell; this is a yes / no question coming from the line before it and the presence of "short form + の + かい".
でもたまに思い出し、お前に問いかける
憎しみより深い幸福はあるのかい
Does it mean, "But sometimes I remember and I ask you if happiness (幸福{こうふく}) more profound (深{ふか}い) then hatred (憎{にく}しみ)?"?
"Is there a happiness more deep than hatred?"
Perhaps breaking it down would help:
深い幸福 - deep happiness
深い幸福はある - There is a deep happiness
深い幸福はあるのかい - Is there a deep happiness?
憎しみより深い幸福はあるのかい - Is there a deep happiness that is deeper than hatred? OR Is there a deep happiness that is more so (より) than hatred --> "Is there a happiness more deep than hatred?"
