It does not seem as if the Vice President's wife is called the Second Lady. If you go on the White House's Website there are sites for the President, Vice-President, First Lady, and Dr. Biden... not the Second Lady.
For better or for worse, there is no official designation for the Vice President's Wife. Sometimes she is called Mrs. Vice President or the Second Lady, but not officially.
But if you click on her name, they refer to her as the second lady in the summary of her life. add a comment