Title kind of says it all. Mussolini and Hitler initially hated each other's guts.
The precise reasons don't really matter too much: perhaps Mussolini was just a bit smarter, maybe Hitler insulted Mussolini's mother at a Fascist powwow or something that both were attending some time in the '30s.
The end result is that Mussolini does not do anything to support Hitler and the Nazi party. At best, he ignores him; at worst, on the diplomatic stage he acitively opposes him.
For the sake of argument, he still supports Franco in Spain (ignoring Germany as much as possible while doing so), and should WWII still break out in 1939 ITTL, Italy remains (initially, at least) neutral.