That is precisely the paradox I am exploring. Joseph's brothers' wills were entirely free in their actions, and God enacting his own will accomplished precisely what he intended. It says nothing about Joseph's brothers being steered or coerced to do what they did, they were free. Yet the result of their actions was what entirely what God intended for good. It seems that could be applied to all of redemptive history.
The Bible continually speaks of human responsibility for choices made, which can only exist if the choices were made freely without some irresistible divine manipulation. The Bible never suggests that all of people's choices are controlled or ordained by God. Nor does it indicate that all of men's choices are totally free. After all, God did harden hearts, from time to time. But God never hardened the heart of a man who had not previously, by his own series of unfettered choices, already set the trajectory of his own life toward a collision course with God's judgment.
Joseph's brothers, to be sure, inadvertently played into God's plans—but there is no indication that God was feeding choices into their will at the time. They hated Joseph. All God had to do was to place Joseph at their mercy, and their own hatred would take its course. God did not sovereignly ordain that they would hate Joseph. If for any reason, Joseph's brothers had experienced a momentary crisis of conscience before selling Joseph into slavery, and failed to do so, there were certainly plenty of other ways God could have arranged for some other circumstance (being kidnapped by Midianite traders comes to mind as one alternative) to get Joseph into Potiphar's house.
The same is true of Judas, Caiaphas, and others involved in Christ's arrest and crucifixion. They fulfilled God's purpose without realizing it. However, there is nothing in scripture suggesting that God turned them against Christ. They had been planning to kill Him since the beginning of His public ministry. Until that final Passover, they were divinely prevented from doing so, because "His hour was not yet." When the proper time came, God removed His protection and "delivered" Jesus to them (Acts 2:23). God did not need to interfere with their freedom of choice, the trajectory of the choices they had already made and were making over a three year period rendered it predictable that, given the freedom to act upon their own plans, Jesus would be crucified—thus fulfilling God's purpose.
Even if God, in these two cases, and possibly a few more, had sovereignly made these people sin in the ways they did (an entirely unnecessary theory), we have to admit that these were special, world-changing cases, in which God might make an exception to his general hands-off policies. It would not suggest that He also determines everyone's choices (for example, their choice to believe or not to believe the gospel). The Bible nowhere suggests that God interferes with, or has preordained, all human choices.
I don't see how we can say that there is one God who exists in three persons, without changing the definition of one so much that it is no longer one. But I believe in the Trinity. I don't think we have to be able to wrap our mind around every mystery and paradox that we find in scripture.
To say that Adam and Eve were "one flesh" (though they were two persons) does not present a paradox, nor a mathematical problem. We understand that calling them "one" is referring to a different aspect of their being from when they are referred to as "two." There is nothing that defies logic in it. It is just a question of deciding what aspect of their existence is being described when saying they are "one flesh" (we have no problem understanding what is meant when we speak of them as two).
To say that God is "one" is similarly open to interpretation. There are those who interpret according to "Oneness Pentecostalism" or modalism, there are also Arians, as well as those with various trinitarian interpretations. All of them see God as "one", but have different understandings of what that means. Similarly, modalists and trinitarians would have differing understandings of what it means to say that God is "three."
"One in substance, three in person," is the trinitarian standard explanation. While it leaves the terminology questionably defined, yet it does not present a logical contradiction, so long as the "oneness" and the "threeness" of God are describing different aspects. It would truly be a contradiction (and necessarily false) to say that God is both one and three,
in exactly the same sense! To say that man is freely choosing his actions, and that God is determining what he will choose, on the other hand, is contradictory—and necessarily false.