Well, to give you a quick answer, Germany has allowed a much weaker France to call the shots in the EU after WWII, despite being a much stronger economical power. In exchange, France facilitated Germany's rehabilitation.
As to this challenge:
Much like Germany, Italy's economy operated at considerable lower efficiency levels than it could have, for political reasons. Secondly, Mussolini was an idiot who mismanaged the war on an even grander level than Hitler did. If he had actually wanted to screw up his war effort, he could not have done a better job.
So how can this pan out? Let's assume the Italians do a little bit better in WWI, sufficiently to be a major player in the post-war peace negotiations. And let's assume Italy blocks the punitive reparations demanded by France. This would garner Italy considerable goodwill in Germany and Austria.
OTL, Hitler was a great admirer of Mussolini and Germany actually was the junior fascist partner of Italy for awhile and backed down over Austria in the 1930s under Italian pressure (until France and Britain forced Italy in a Italo-German alliance).
But while Germany's economy bloomed, Italy's stagnated under corrupt and incompetent leadership and strategies.
It wouldn't take too much changes to have Italy perform to its potential in economic and military issues. Perhaps Mussolini's power and influence is curtailed by the Fascist council and the unhealthy relationship between industrialists and the fascists is cut. Or the King develops a backbone. Nah, that would be ASB but perhaps the army clips Mussolini's wings when he tries to raise the blackshirts in a rival organization.
The Italian army was actually quite good by late 1930s standards. Its problem was that Mussolini enlarged it beyond the limitations of its manpower pool and industrial output, leading to a large army with insufficient, outdated equipment and poor leadership. A smaller army of higher quality would improve their chances. And a more focused strategy which played to their strengths instead of scattering their forces and focus. Instead of major campaigns in North Africa, the Balkans and Russia which was beyond Italy's logistical capacity, a campaign in a single theatre would have been well within their abilities and would have placed their opponents in difficulties.
Just imagine a properly motorized Italian army in North Africa, with sufficient supplies.
Could such an Italy have dominated Germany? No, but then Germany did not dominate Italy from the start either. Italian weakness sucked Germany into the Italian war effort and eventually forced it to prop up the faltering Italians.
Had the Italians done better, they would have been top dog in their own sphere of influence and could well have been an equal partner in European affairs.
