I’m a bit unclear on the difference between natural law theory and divine command theory. After all, natural law thinkers do believe in authoritative divine commands.
Your confusion is understandable, because some writers use the expression “divine command theory” for any theory which believes that there are such things as authoritative divine commands. But that way of using the term is misleading. In the proper sense, a divine command theory is a theory which believes that the authority of a divine command depends on the naked will of God, apart from His wisdom and goodness. The classical natural law tradition rejects this view, because God’s will is not naked. It cannot be separated from His wisdom and goodness.
We might approach your question through the Euthyphro dilemma: Does God command what is good because it is good, or is it good just because He commands it? The former answer denies God’s sovereignty: It puts God in subjection to the Good. The latter answer – which is the answer of divine command theorists -- rescues God's sovereignty, but at the cost of making the Good arbitrary. Divine command theory embraces the latter answer. The classical natural law tradition rejects both answers in favor of a third.
Each alternative draws most of its plausibility from the plain wrongness of the other. But notice that they share a tacit premise: They both assume that God and the Good are different things. Classical natural lawyers deny this assumption. God simply is the uncreated Good. To turn the idea around and look at it from the other direction, if we inquire deeply enough into the Good, what we find is not a what, different from God, but a Who, God Himself in person.
Here is how this view of God connects with natural law theory. What we call “nature” is an ensemble of finite, created goods which reflect God’s infinite, uncreated goodness. The pattern by which He made and governs these created goods, as it is in His own mind, is traditionally called “eternal law.” This raises a problem: Finite, created beings like us don’t know this pattern in itself. But there is a solution: We can know it in its reflections. One such reflection of eternal law is explicit, verbal revelation, traditionally called “divine law,” though this term is misleading, because all of these arrangements are divine in origin. The other is the order of creation itself, as our created minds behold and participate in it. And this is traditionally called “natural law.”
One old-fashioned way of speaking of these two reflections is the “book of scripture” and the “book of nature.” Divine law, the book of scripture, conveys divine commands by putting them in words. Natural law, the book of nature, conveys the commands of the same God by embodying them.
But this is not what is called “divine command theory,” because the divine commands derive their authority not from a will which says “Do it because I say so,” but from a will united with supreme wisdom and goodness. Does this clear up the difference?