Now for your Michael Duggan. Note: there are at least 3 Michael Duggans with wife Catherine in Manhattan at the same time!
Michael Duggan married 26 June 1895 Manhattan to Catherine Collins (Italian Genealogy website NY marriages)
1900 Census- Manhattan
Michael Duggan, Mar.1867, Ireland, to US 1893, driver
wife Catherine Duggan, July 1870, Ireland, to US 1895, 3 ch./2 liv., m.5 yrs
dau. Mary Duggan, June 1899, NY
Note: think it should be 3 children/2 died
Naturalization- 19 April 1900. Michael Duggan, age 33, driver, British citizen, arried NY Oct.1893.
1910 Census- Manhattan
Michael Duggan, 42, Ireland, to US 1895, salesman-brewery
wife Catherine Duggan, 40, Ireland, m.14 yrs, 6 ch./4 liv., to US 1893
dau. Mary Duggan, 10; dau. Margaret Duggan, 8; dau. Josephine, 5; son John J., 3 (all b.NY).
1920 Census- Manhattan
Michael Duggan, 52, Ireland, wid., to US 1890 Na.1899, engineer R.R.
dau. Margaret, 19; dau.? Joseph?, 16; son John, 13 (all b.NY, parents both b.Ireland).
1930 Census- Manhattan (in household of David Stryker)
Michael Duggan, 52, Irish Free State, to US 1890 Na., engineer- office building. Also dau. Margaret age 29.
Note: since the 1930 census was taken after the Partition of Ireland this indicates Michael was born in one of the 26 counties in the present Republic of Ireland.
Mary A. Duggan married 21 Apr.1919 Manhattan to David P. Stryker (from Italian Genealogy website N.Y. marriage index)
ALL of these U.S. details match your family. There is NO mention of Sheffield (or anywhere else in England).
I looked for birth in IRELAND for Michael Duggan but not enough info to make a match even with month and year. Same problem with Catherine Collins.