Now you are saying to yourself, how in the heck is he going to link this one into the Carman family?  Well it is not all that hard.

"In 1883, a tin mine, the Etta, was opened, which caused excitement among Eastern investors, Shortly after, James Wilson, a New York mining promoter, engaged Professor Gilbert E. Bailey, state geologist of Wyoming, to examine mining claims in the area where Keystone was later located. In need of talent, as well as geological advice, Wilson hired Charles E. Rushmore, a young but able New York attorney, to check the titles to properties on which Bailey reported favorably. Although an Easterner, Rushmore quickly made friends among the miners and prospectors. One day he was returning to headquarters of the Harney Peak Consolidated Tin Co., Ltd., located at Pine Camp, which was north of the great granite peak soon to bear his name. With him were a local business man, and William W. Challis, a prospector and guide. As they neared this spectacular mountain, Rushmore turned to Challis and asked its name, Challis jestingly replied: "Never had any but it has now - we'll call the damn thing Rushmore". Thus in 1885, the chance remark of a rough miner to a visiting lawyer, fastened a permanent name to the mountain. The United States Board of Geographic Names officially recognized the name "Mount Rushmore" in June 1930." Forty years later, Charles E. Rushmore donated $5000 towards Gutzon Borglum's sculpture of the four presidents' heads on the mountain - the largest single contribution. The Memorial was dedicated by President Coolidge on August 10th, 1927." - "Mount Rushmore", by Gilbert C. Fite, 1952, University of Oklahoma Press. 

So where is the Carman connection in all this?  Charles Rushmore, who Mount Rushmore was named after is the son of Edward Carman Rushmore, who was the son of John Rushmore who was the son of Carman Rushmore, son of William Rushmore and Mary Carman.

Mary Carman is the daughter of Benjamin Carman and Mary Bedell.  Carman Rushmore names one of his sons Benjamin Carman Rushmore. Carman Rushmore's daughter Ann marries Samuel Snedeker. Samuel Snedeker is the son of Abraham Snedeker and Nancy Carman. Nancy Carman is the daughter of Samuel Carman and Mary De Mott. Samuel Carman is also a child of Benjamin Carman and Mary Beldell and therefore brother of Mary Carman.

Oh, Charles Rushmore was fairly well off, as the story implies. He had a large estate near Tuxedo Park, New York at Woodbury Falls - the name of it was "Car-more".