Upvote:3
Hitler did, in fact, go to war with Italy, de facto, if not de jure. His "excuse" was to restore the "rightful" Italian government (under Mussolini). This was after the Italians rebelled and went over to the allies in 1943.
If the Axis had been winning, the Italians might have rebelled (against Mussolini) anyway, because of the hardships of the war. In 1945, the British "rebelled" (peacefully) against Winston Churchill by throwing him out of office in favor of Clement Atlee. A similar thing might have happened in Italy after the Axis won, with Hitler sending German troops into Italy to restore Mussolini. Of course, it would have been cast as "bandit suppression," or something similar, as opposed to a declaration of war.