There is a whole subgenre of stories about future archeologists misinterpreting our time. A bunch of those stories are reviewed in Gary Westfahl's Locus article "The Addled Archaeology of the Future". If your mother is remembering one of the stories in that article then, based on the Statue of Liberty being involved, it's probably either James A. Mitchell's The Last American:
Like Poe's letter-writer, the Persians often misinterpret what they find in these cities. Seeing a sign on the hotel Astor House, the narrator assumes that Astor is "the name of a deity, and here is his temple." They assume that the purpose of the Statue of Liberty was to cast light on the city and cannot believe one of their men who visits it and reports that there are no signs of lighting devices. They come upon the surviving pillars that once supported one of the great bridges of New York, but noting how far apart they are, they conclude that this could not possibly represent the ruins of a bridge. Observing the statues of Native Americans that once stood outside cigar stores, the writer's comment is, "How these idols were worshipped, and why they are found in little shops and never in the great temples is a mystery." It is significant that these future Persians, like later archaeologists we will encounter, have a tendency to interpret enigmatic buildings and objects as aspects of a primitive, polytheistic religion; clearly, it never occurs to these Moslems that the ancient Americans might have practiced their own form of monotheism.
or else Robert Nathan's The Weans:
As one example of their faulty conclusions, the archaeologists assert that "The Weans were probably not at all a friendly or hospitable people" based solely on two pieces of evidence. First is New York City's Statue of Liberty, whose "one arm upraised" is interpreted as a sign of "a threatening attitude." Second is the discovery of an "inscription" reading "the dodgers were shut out." This reference suggests that Nathan's explorers are examining not only buildings and artifacts but also written documents: a table of baseball statistics, evidently found in a newspaper, is regarded as "a primitive form of banking," and there are a number of garbled references to literary writers such as Henry Wadsworth Longfellow, Ernest Hemingway, William Faulkner, James Joyce, and Dylan Thomas. Their other errors include: rendering the name of the city of Washington as "Pound-Laundry"; interpreting the name of labor leader Jimmy Hoffa as a common noun, "hofa"; and assuming from the term "hot dog" that the Americans "ate dogs, roasted." Again, the archaeologists are overly anxious to see evidence of primitive, polytheistic religions: they assert that "each city-state worshipped a different Divinity"; a fragmentary description of a rock'n'roll concert is thought to concern a religious event; and the once-influential gossip columnists Hedda Hopper and Louella Parsons are conflated as "a powerful Divinity named Hedda, or Lolly."
The quotations are from Westfahl's article.
Mitchell's The Last American was published in 1889. Nathan's 1960 book The Weans was based on two short stories, "Digging the Weans" (Harper's Magazine, November 1956) and "A Further Report on the Weans" (Harper's Magazine, April 1959). However, if your mother is sure her book was set a mere 100 years in the future, then it can't be either of these: Mitchell's book is set in 2959, Nathan's 6000 years in the future.
