Although I have no proof that this is the case, I believe that the reference to Garcia in Cheaper by the Dozen is a reference to the 1899 essay (and perhaps the 1936 movie that was based on it) called “A Message to Garcia.”
The story of the message to Garcia came from the time just before the Spanish-American War of 1898. Before the war began, the president of the United States, William McKinley, wanted to get in touch with a Cuban rebel leader named Calixto Garcia. He sends a young American officer named Andrew Rowan to deliver a message to Garcia. Rowan makes his way through dangerous conditions to get to Garcia.
The context of the reference to Garcia in Cheaper by the Dozen implies that it is an allusion to this story. The narrator says that, when Dad decided that he wanted to talk about some particular topic, he would (p. 39 in my copy of the book, toward the end of Chapter 6) “head toward it as relentlessly as if Garcia were waiting there…” In other words, he would overcome any obstacles in his way to move (metaphorically) in the direction he wanted the conversation to do. In this way, the author is using the allusion to Garcia to show how doggedly his father would pursue his chosen topic.
The story of the message to Garcia would have been relatively well-known when this book was written in 1948. It even stayed around long enough to figure in the title of the Looney Tunes cartoon “A Message to Gracias” made in 1964. Because this story matches with the idea of the allusion in the book, and because it should have been well-known when the book was written, I believe that the reference to Garcia in Cheaper by the Dozen is supposed to refer to “A Message to Garcia.”