Aunt Jane's Nieces and Uncle John picks up the continuing story of the three cousins Patsy Doyle, Beth De Graf, and Louise Merrick, and their family; the plot of the book begins three days after the wedding of Louise and her fiancé Arthur Weldon, the event that concluded the fifth book in the series, Aunt Jane's Nieces in Society. The sixth novel begins, as per pattern, with the cousins' Uncle John getting an inspiration for a new adventure: in this case, the family will escape a cold New York City winter by taking a trip to southern California, the land of "sunshine and roses." Since Louise is away on her honeymoon, she is effectively left out of the story; her place is taken by Major Doyle, Patsy's father – the first time that the Major accompanies the young people on their escapades. (The Major is relieved that Uncle John has set his fancy merely on California, and not "Timbuktu or Yucatan...Ethiopia or Hindustan....")
The four travelers (accompanied by Mumbles, Patsy's new puppy) reach Denver by train; along the way, they meet an appealing teenage girl (14 or 15 years old) named Myrtle Dean. Myrtle is a poor orphan; she was injured in an automobile accident, which inhibited her ability to walk. She had been living in Chicago with an aunt, and earned her living by sewing. But now, Myrtle has been sent West by her unsympathetic aunt to find a missing uncle named Anson Jones – though neither woman knows if the uncle is still in Leadville, Colorado, his last known address, or if he will be able to care for the girl if she finds him. Patsy and Beth are shocked at her situation; it is clear to them that the aunt has abandoned Myrtle to her own inadequate resources. Uncle John telegraphs ahead, and discovers that the mysterious uncle has left Leadville for parts unknown. Patsy and Beth then adopt Myrtle as their "protégé," and take her with them on their trip. They buy her new clothes, and she shares their hotels, meals, and adventures.
(Baum cannot resist the fairy-tale viewpoint, and "Edith Van Dyne" gives a plug for the Oz books: Myrtle is "amazed and awed by the splendor of her new apparel, and could scarcely believe her good fortune. It seemed like a fairy tale to her, and she imagined herself a Cinderella with two fairy godmothers who were young and pretty girls possessing the purse of Fortunatus and the generosity of Glinda the Good.")
Uncle John buys a large, seven-passenger touring car and outfits it for camping and cross-country travel. He also hires a chauffeur, a half-Indian Québécois named Wampus. The chauffeur provides some of the comic relief in the story, though he is also presented as highly competent, courageous, and principled, a "brave and true man." (Baum employs another comic chauffeur in the final book in the series, Aunt Jane's Nieces in the Red Cross.)
The party sets off by car from Albuquerque; they visit the Grand Canyon and the Navaho and Hopi reservations. They witness a performance of the Hopi snake dance. In western Arizona they are waylaid by a riotous group of cowboys, who refuse to let them pass until the girls join them in a dance. In what grows into an ugly incident, the travelers are forced to acquiesce – at first; but Patsy and Beth, typically clever and resourceful, develop a plan to defeat their opponents and escape.
The group reaches California, none the worse for wear; they are delighted with the change of scene. They make the Hotel del Coronado in San Diego their headquarters. (This is another bit of autobiographical writing for Baum; he stayed regularly at the Coronado during trips to California.) Myrtle Dean has proved a delightful and rewarding companion; her health has already shown signs of improvement with better diet, less anxiety, and the warmth of new friendships.
Myrtle, however, has been the center of a series of curious events. At the Grand Canyon, the travelers saw a morose-looking man standing at the very lip of the canyon; Myrtle, fearing that he intended to jump, cried out to him, and the man turned away from the edge. At San Diego, they once again see the strange man, standing on a cliff over the ocean; Myrtle once again fears his suicide, and cries out to him. The man turns out to be staying at the Coronado; his name in C. B. Jones. Myrtle happens upon him a third time, and takes away the revolver he has been brooding over in his room.
After the three incidents, the man becomes emotionally attached to, if not fixated upon, Myrtle. Uncle John's inquiries reveal that the man, Collanson Jones, is the "Anson" Jones who is Myrtle's missing uncle. The two are happy at this re-unification of their sundered family, and Jones's deep melancholy is relieved (the evil aunt who sent Myrtle away had told him the girl was dead). And since Jones has made his fortune in mining, Myrtle's financial future is secured.

Question: Why did Patsy and Beth dance with cowboys in Arizona?
Answer: the cowboys wouldn't let the family pass unless the girls danced with them
Alternative answer: The cowboys refused to let them pass without a dance