Respectfully,

God's will for the common (not "neutral") kingdom is revealed in general revelation (creation [Rom. 1], conscience [Rom. 2], and providence [Acts 14:17]), and in special revelation (Genesis 9).

"Here we have no continuing city," brother, and the church is to extend the kingdom by persuasion (the word), not coercion (the sword). We are pilgrims in exile and will be until our King returns. 

Until then, the church is Rahab in a cosmic Jericho, praying "thy kingdom come"--she does not "bear the sword," nor should she grasp after it. 

I agree that there is no epistemological dualism at play here, but there is an eschatological "dualism" of sorts: there is the "already" and the "not yet." We should not "immanentize the eschaton" -- that has gone very, very badly in the past and for good reason: it is error.

I'm not sure what your confessional commitments are, but the Westminster Standards (American Revision) make it clear that the church and the civil powers are distinct governments with different powers, means, methods, and ends.

Perhaps you've already done a ton of reading in the "opposition," but if you haven't, I'd encourage you to engage with Vos, Kline, Clark, Hart, and especially VanDrunen on this question. Either way, it is most certainly not a "hatred of God's law" that fuels opposition to theonomy/theocracy--it's theological conviction.