It was "The Crown Snatchers" by Bernd Eilert and F. K. Waechter, originally published in German, it was published in English in around 1975.
The story begins by introducing itself as a made-up story. It introduces the three children as the principal characters and considers a number of settings before deciding on a meadow. It turns out that the meadow lies within a small kingdom inhabited by the three children and a variety of anthropomorphic animals. We find Robert, Joanna, and Moritz hard at work trying to reach hazelnuts in three tall trees. They make the acquaintance of a dignified owl, Dr. Loy, who is suddenly scared off by the sound of an approaching motor. The children watch bemused as King Fatback's royal limousine approaches. The King himself, a pig, accuses them of stealing his nuts....
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The children reach Dr. Loy, present him with the crown, and ask him to be the new king. He accepts, and the next day he holds a meeting with all the townspeople. King Loy changes the kingdom's motto from Let the People Serve the King to Let the King Serve the People, and announces that each citizen may choose his or her occupation. Thus, the kingdom shifts from totalitarianism to a constitutional monarchy.
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Soon after, the king awakes to discover the crown is once again missing. He calls a meeting of all the people under the assumption that the thief or thieves will not appear. Sure enough, the children are among the absent. After much speculation, the children appear with Holger and friends. They carry a bag that makes odd clinking sounds. They have changed the monarchy into a democracy by melting the crown down into many small crowns, one for each person.