In OTL, the Netherlands came close to having their own analog of the Vichy regime. After the Dutch government had evacuated to Britain along with the royal family in 1940, the prime minister, Dirk Jan de Geer, wanted to return to German-occupied Netherlands, but he was preempted by Queen Wilhelmina:
One possibility:
I'm assuming she would be succeeded by her daughter Juliana, unless she's killed in the same incident, in which case it seems the legitimate heir would be Grand Duke Wilhelm Ernst, who on top of being German was also a sadist. But since he died in 1923, there would probably be a succession crisis, and I'm not familiar enough with dynastic rules to figure it out.
Further, is it likely that a "Free Dutch" faction pulls a De Gaulle and sets up its own government-in-exile?
When in London, De Geer advocated negotiating a separate peace between the Netherlands and the Third Reich. He damaged the Dutch government and the Dutch morale by openly stating that the war could never be won. He was finally removed from office on the instigation of the iron-willed Queen Wilhelmina, and replaced by Gerbrandy.
Later on, he was sent with a diplomatic package to the Dutch East Indies, present day Indonesia. He never arrived there: on a stop-over in Portugal he left, and returned to his family in the Netherlands with the permission of the Germans. This greatly angered Queen Wilhelmina, who called him a traitor and deserter to the Dutch cause. He later wrote a controversial leaflet with "instructions" for the people on how to cooperate with the Germans.
What if in TTL Wilhelmina dies of whatever causes before the beginning of WW2? A less iron-willed monarch (and one more scrupulous about respecting constitutional procedures) would probably have failed to stop the government returning to The Hague.One possibility:
Civil unrest gripped the Netherlands after the war, spurred by the 1917 Bolshevik revolution in Russia. Socialist leader Pieter Jelles Troelstra wanted to abolish the existing government and the monarchy. Instead of a violent revolution, he hoped to do this by winning control of Parliament in an election, supported by the working class. However, the popularity of the young Queen helped restore confidence in the government. Wilhelmina brought about a mass show of support by riding with her daughter through the crowds in an open carriage.
A monarch riding through a city gripped by civil unrest in an open carriage--there are precedents of such an idea ending in grief.I'm assuming she would be succeeded by her daughter Juliana, unless she's killed in the same incident, in which case it seems the legitimate heir would be Grand Duke Wilhelm Ernst, who on top of being German was also a sadist. But since he died in 1923, there would probably be a succession crisis, and I'm not familiar enough with dynastic rules to figure it out.
Further, is it likely that a "Free Dutch" faction pulls a De Gaulle and sets up its own government-in-exile?