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You don't mention Joseph's approximate age? This may be wrong family but just in case there is this family in Syracuse, Onondaga, New York in 1930 with step child Joseph McCauley. All listed as born England and most came to USA in 1928
George P Marshall 45 b England Labourer
Rose A Marshall 49 b England
Olive Marshall 10
Patricia Marshall 8
J Charles Mc Cauley 27 stepson
Albert J Mc Cauley 26 stepson
Dorothy A Mc Cauley 21 stepdaughter
Joseph T Mc Cauley 18 stepson
And a previous marriage in Llanhilleth of a Rosa Ada McCauley age 36 Widow (Father Charles Galton) and George Marshall 34 Soldier (father Robert Marshall) in 1917 ties the family possibly into yours
https://familysearch.org/ark:/61903/1:1:KCTJ-1VTKay
Edit in 1940 both J Charles McCauley and Joseph T McCauley above were living together in Sidney, Delaware, New York with birth places listed as Wales
Joseph C McCauley 37 Proprietor Retail Parts?
Althea McCauley 40 b New York
Richard C McCauley 1 New York
Joseph J McCauley 28 Engineer