Jane (Young) Cairns might have gone to Scotland then Ireland then to U.S. but this is not yet proven.
1870 census- New York, New York
James Cairns 30 Ire. hackdriver; Jane Cairns 30 Ire.; Mary A. Cairns 9 Ire.; William J. Cairns 7 Ire.; James Cairns 5 Scot.; Samuel Cairns 3 Ire.; Jane Cairns 1/2 NY.
1880 census- Pittsburgh, Allegheny, Pennsylvania
James Cairns 40 Ire. teamster; wife Jane Cairns 42 Ire.; dau. Mary Cairns 18 Ire. nursing; son William Cairns 16 Ire works at gold plating; son James Cairns 14 Scot.; dau. Jennie Cairns 8 NY; son Samuel Cairns 7 NY; son George Cairns 2 Penn.
1900 census- Indianapolis, Marion, Indiana (1920 census gives 1866 as date to U.S.)
James Cairns Oct.1865 Scot.; wife Nellie 30, son Harold 9, son Albert J. 2; dau. Jennie 7.
Wonder if George Shepherd Cairns, bapt.1878 Pittsburgh, parents James & Jane is the 2 year old George Cairns in 1880 census?
https://familysearch.org/pal:/MM9.1.1/V2FT-5YH