Mussolini was Italian too, you think he'd answer anything but "yes sir" if Hitler told him to level the Vatican.
Also, look at what happened in Catholic France in the eighteenth century, and in Catholic Spain and Mexico in the twentieth century. Sometimes Catholic countries are the Church's worst enemies.
Suicide for Il Duce...
The RCC superceded even the authority of Mussolini, who would have been hung 4 years early had he followed such a directive.
IF the Pope had spoken up against Nazism, Hitler would have indeed found himself in a conundrum.