This requires changes likely as early as the Anschluss issue, there was a point in time during which Hitler and Mussolini's status as Axis buddies for life was in serious jeopardy, mostly over conflicting spheres of influence in Austria, Hitler wanted his homeland back, Mussolini didn't want Austria falling into the German sphere of influence, but by the time Anschluss happened Mussolini had written them off.
Earlier though, when Germany was not ready for war and Italy had a stronger military... things could have gotten nasty.
I also agree with Cook that allied Italy is pretty unlikely unless you go really far back, neutral Italy that just sort of watches the world go by and quietly lets German shipping refuel at Italian ports while looking for prize pieces of various countries to snag up during the war (like Slovenia) is more possible.