No way that could have happened!
If Nothing Else, the Soviets would NEVER surrender their share of occupied Germany to the Allies. Stalin was hell bent on his sphere of influence, that's why we had Prussia and Saxony as vassals, as well as territorial revisions in favor of Poland and Czechloslovkia in the works.
You've forgotten, of course, that Austria became independent and that Elass Lotheringen was restored to France--but I don't see any "Unifed Germany" occupying either of these areas, or being allowed such.
The Question isn't whether the Allies are going to punish Germany for WW2--it's how much. There was a plan called the Morganthau plan that probably would have been executed if Germany remained unified--it called for the forced deindustrialization of Germany and leaving it in a state of economic poverty. Of course, this would have forced the Germans to beg for help from the Soviets, and nothing like this would have be accepted.
I suppose, for a PoD, you'd need 1941, where the German Wehrmacht takes Moscow instead of moving to the Gomel Pocket, and then have an equally victorious 1942 and 1943 where the Germans advance to the Volga and into Baku--and then the Soviets hammer the Germans blow by blow all the way back into the Dnieper by 1947. By this time, however, the Allies have detonated 20 atomic weapons against Germany, and Germany surrenders to the Allies, leaving Germany in one piece, as well as leaving the Soviets with their 1938 borders.
Then you'd have a postwar world where Germany would be entirely administered by the Allies and they could choose to have one Germany (perhaps including Austria, now I think about it). Said Germany is basically going to face permanent occupation by the allies and probably forced into paying a flat tax to the allies to cover the occupation and as a source of compensation. Oh yeah, the Allies would undoubtedly punish Germany territorially as well, but it would remain one (smaller) piece.
German culture and the image of what it means to be a German has been (Irrevocably) damaged by the entire Nazi movement--that they have stooped lower than any nation for two hundred years means that perhaps their pariah status would be appropriate. In any case, a friendly Poland, Netherlands, Czech State (would it be reunified?) and France would ensure that Germany will never be a threat to the world again--and in all likelihood, the specter of the Atomic Bomb is behind this threat. The Germans had exterminated entire cities in their sick war of conquest, killed tens of millions of civilians. If simply cold war politics didn't demand it, the German people would live in a state of Justice.
It would be a cruel order, but perhaps a hundred times as fair as they themselves had wanted. A unified Germany means that there is no reason NOT to punish the German people for their trangressions against the world. There would be a rump Germany with high taxes to compensate the nations it had abused and police forces to enforce a new order. One could only hope that perhaps 50 years afterward, such policies could be rescinded.