Not a book, but possibly a good source for the quick overview you're looking for... if you can get the History Channel, whenever they're not running garbage (ancient aliens), they're usually running something on WWII. It's quite a popular subject, and draws viewers.
They recently ran a series called The World Wars that followed a number of key individuals through both conflicts: Hitler, Stalin, Roosevelt, Churchill, Mussolini, Tojo, Patton, and MacArthur. I had an issue with a few of their facts, but I also learned some new things. It was recommended to me by adults already familiar with the historical basics, and I'd recommend it to a child just beginning to get a sense of the time.
It's available for purchase if it's not available to you in other ways, and their website has a number of other resources you might be interested in as well.
