In reading a biography on Jonathon Edwards I've found that he too wrestled with these questions. In the book the author quotes Edwards saying he was, "full of objections against the doctrine of God's sovereignty, in choosing whom he would to eternal life, and rejecting whom he please; leaving them to eternally perish, and be everlastingly tormented in hell. It used to appear like a horrible doctrine to me." ("Personal Narrative," Works, 16: 791-92)
The key to Edwards transformation from resistant to convinced of Calvinist doctrines is his relentless pursuit of Scripture and, even more primary, the undetectable work of the Holy Spirit in his life. By working through his questions Edwards came to a point where he suddenly believed and it all was settled in his mind and soul.
It was not an intellectual, reasonable decision. It was the settling of his mind by God. As Edwards would later write, "never could [I] give an account, how, or by what means, I was thus convinced; not in the least imagining, in the time of it, nor a long time after, that there was any extraordinary influence of God's Spirit in it: but only that now I saw further, and my reason apprehended the justice and reasonableness of it." ("Personal Narrative," Works, 16: 793) I understand Edwards here because this is very much the story of my own Calvinist conversion.
As humans being we have a difficult time with our inability to comprehend God in his totality. In our efforts we often end up putting God in a box or developing weighty philosophical ideas to try define who God is and what he does. While we should study and strive to know more of God, (Luke 10:27) we must also remember that all things will not be made known to man this side of heaven (1 Cor 13:12).
In a recent blog post John Piper touches on God's sovereignty in all things, the existence of sin, and the role of man in understanding it. Here is a snippet of his article,
We don't need to know how he does it to believe it and rest in it and worship him for it. This will not be an easy sentence for many. And there is nothing I can do to prove its truth. My only recourse is to pray that if you wrestle with this doctrine that you will wrestle equally hard in the Scriptures, and that the Holy Spirit may open the eyes of your heart and mind, as he did to Edwards long ago, and as he has done in more recent times with me.
One of the main points of the forthcoming book Spectacular Sins and Their Global Purpose in the Glory of Christ is that sin and God’s wrath against it were part of God’s plan when he created the world. This is different from saying that God sins or that he approves of sinning.
... And we don’t need to know how he does it to believe it and rest in it and worship him for it.