God has basically two distinct "wills", a "sovereign will" and a "moral will".... God has a "moral umbrella" that He warns us to stay under. If we choose to go outside that "moral umbrella", we will suffer the moral consequences. That does not mean we will lose our grace, it just means we suffer. But it is still a choice we make everyday. God's Soveriegn will....TOTALLY DIFFERENT. God chooses who He chooses. God ALLOWS evil into someones life if He chooses to (ie. Job).
An example of a moral consequence would be if you chose to cheat on your taxes and got caught. God did not will that to happen. That was a stupid choice you made. If you get caught you will suffer that consequence. In other words, choose to sin choose to suffer. Now, compound that by all the other stupid choices non-beleivers and beleivers make with regard to moral choices. That is why we suffer. This does not take away from God's overall Soveriegnty in any way.
Another example is weather patterns. If a tornado comes by and kills people in its path, that was not God's will. Yes, God can certainly create natural disasters if He wants to, however, that doesn't mean He desires (wills) to use that method. The bible never teaches that God creates all natural disasters in the world. The bible does state that when the "fall of man" happened, the earth fell with him ("creation groaned"):
note: creation = earth in the verses below....
Rom 8:18-22
18For I consider that the sufferings of this present time are not worth comparing with the glory that is to be revealed to us. 19For the creation waits with eager longing for the revealing of the sons of God. 20For the creation was subjected to futility, not willingly, but because of him who subjected it, in hope 21that the creation itself will be set free from its bondage to decay and obtain the freedom of the glory of the children of God. 22For we know that the whole creation has been groaning together in the pains of childbirth until now.
That being said, God does work in mysterious ways in our world daily. The bible promises that whatever happens in the world, God can take that and work it for good (ROM 8:28). That is the basis of our faith and hope and ability to cope with a "broken" world. There is nothing that is beyond God's power to redeem and use for His purposes.