Neutral nations were not immune to Hitler's treaty breaking. Turkey and Switzerland were among the first victims to fall prey to Europe's German and Italian hegemons.
Turkey was invaded because German intelligence caught wind of secret negotiations between Ankara and Washington to form an alliance. The Turkish majority in Istanbul were deported, and the city was re-populated with Greeks and its name reverted to Constantinople. Switzerland's harsh mountainous terrain, determined conscript military, and complex fortifications proved a challenge for the German and Italian invaders.
Hitler and Mussolini also supported Franco's Invasion of Portugal, Britain's oldest ally.
With the loose ends of Turkey, Switzerland, and Portugal tied up, Hitler double-crossed Mussolini. Italy was reduced to OTL's Italian Social Republic (Northern Italy.) Because Spain was the first nation to recognize the Italian Social Republic, Spain was awarded Sardinia, Sicily, and Southern Italy. (Spain was later re-named Iberia.)
Like Turkey, German intel discovered secret negotiations between Helsinki and Washington. In response, Germany invaded Finland (Lapland War.) Hitler awarded Sweden with Denmark, Finland, and Norway. (Sweden was later re-named Fennoscandinavia.)
Finally there was Ireland, which was invaded because the UK government-in-exile and royal family initially fled there (before having to flee again to Canada.) The Irish Resistance Army (backed by the United States) gave Hitler such a difficult time that he resorted to ethnic cleansing.