Have Dutch Queen being shamelessly Nazi sympathizer, this would cause...
Oh... wait...
This time Hitler won't invade Netherlands, and Netherlands would be Axis aligned. Perhaps being the one who invade and Annex Belgium.
If Netherlands being Axis aligned, Dutch East Indies will then sell their oil and steel to Japan, which will cause no Pearl Harbor. And thus no US cassus belli.
Let's say this time Roosevelt end up invading Japan and Dutch East Indies preemptively.
Oh wait, this would actually cause the public to swing the other way, and FDR end up impeached and US then stops helping allies while paying reparations to Japan and Netherlands.
Which resulted in Axis victory.
And thus the Dutch Monarchy being there to stay.