Before 1912 there were three William Waldorfs. (1848-1919) (1879-1952) (1907-1966). None of them were J J Astor's brother. I'm no genealogy expert, but I'd call them distant cousins.
The line of descent from John Jacob Astor I split at John Jacob Astor III. He and his wife, Charlotte Gibbes, produced the first William Waldorf, who married Mary Paul and established an English line of the family. He was made a Viscount and his title still exists.
John Jacob Astor III had a brother called William, who married Caroline Schermerhorn and continued the American line with J J Astor IV, of Titanic fame.
The whole story is in The Astors by Derek Wilson.
I might add that the story is somewhat confused by the family naming both English and American Astors John Jacob. The son born to Madeleine Astor in 1912 was John Jacob Astor VI, because there was already a John Jacob Astor V in the English line. At last count they were up to John Jacob VIII, born in 1946.