Your lineage is correct with the exception that Patrick Francis Gatens was the son of the immigrant.
Patrick Francis Gatens was born 30 Apr 1878 in Bancroft, Putnam County, WV and married Julia Agnes Murray b. 05 Aug 1887 - 1957 on 19 Aug 1907. (all documented from birth, death, and marriage records)
Patrick's father was William Gatens b. 12 Jun 1849 in McGilden, Scotland. His father and elder siblings were born in Donegal, Ireland. William died in Bancroft on 19 Oct 1893 (Showen Cemetery). He was married to Hannah McMahon b. 22 Dec 1855 - 21 Apr 1933. She was born in Mason County (parents: Arthur McMahon and Julia Cunningham).