There is a passenger list for the Franconia which departed from Liverpool and arrived in New York on 1 Aug 1923 with a Thomas Rae. He was 24, a steel dresser and was destined to Detroit. His closest relative in Scotland was his mother, Mrs. Margaret Smith, 130 Clark Street, Airdrie.
Thomas returned to Scotland on the California which departed from New York and arrived in Glasgow on 4 Aug 1935. He gave 130 Clark Street, Airdrie as his UK address. He also indicated his intended permanent residence was a "foreign country" (that's the column head).
He returned to the US on the Transylvania which departed from Glasgow and arrived in New York on 3 Feb 1936. His listed address is the same as was listed on Jessie's passenger list and the 1930 census. The passenger list also indicates he became a naturalized citizen of the US on 29 Jul 1929.
There is also a passenger list for the Cameronia which departed from Glasgow and arrived in New York on 17 Aug 1936 that lists a Catherine Bell Rae. She was going to join her husband Thomas Rae, 6119 Lakeview Avenue, Detroit. The Lakeview address is crossed out and was replaced with 4515 Crane Avenue. Catherine lists her mother, Mrs. John Rankine as her nearest relative in Scotland.
This information matches a 1940 US census entry for Thomas and Katherine Rae in St. Clair Shores (a suburb of Detroit), Michigan:
http://www.rootschat.com/links/01h6m/ScotlandsPeople has a 1935 marriage in Glasgow for Thomas Rae and Catherine B. Rankine.
Catherine is buried at Forest Lawn Cemetery in Detroit. Here is a picture of her grave marker:
http://www.findagrave.com/cgi-bin/fg.cgi?page=pv&GRid=130853037&PIpi=102856607There wasn't an entry for Thomas and I can't find a death for him.
Jacquie