In 1839 they all boarded the ship "Marion" for the voyage to America.
Elizabeth died on route and was buried at sea.
The trip was "stormy" and apparently nearly went down several times. The ship landed Aug 26, 1839. It took the families 35 days to travel from New York to Chicago by rail, and boat. From Chicago, the travelers proceeded by wagon to Rockford, IL. 
New Life in America
"James Picken had his share of troubles on leaving Scotland with the Giffins on July 4, 1839. His wife died on the ocean and was buried at sea, leaving the husband with three young children" They stayed in Ohio for a year, then came to the Scottish Settlement at Argyll. 
James married Mary Reid about 1847. They had three children:
James Picken, one of the oldest residents of Argyle, died suddenly Friday afternoon. He left his house immediately after dinner and was subsequently found dead in the road. He was 85 years old and was widely respected. 
↑ "Scotland Births and Baptisms, 1564-1950," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:XTJS-MHZ : 10 February 2018), James Pickan, ; citing Southend, Argyllshire, Scotland, reference - 2:16BJFLM, index based upon data collected by the Genealogical Society of Utah, Salt Lake City; FHL microfilm 1,041,076.
James Pickan, Marriage Date: 23 Jan 1833, Marriage Place: Southend,Argyll,Scotland. Spouse: Elisabeth Huie. FHL Film Number: 1041076
↑ "This information comes from a letter written by William Giffen, son of Andrew. William married Margaret Harvey, daughter of William Harvey who came to Argyle in 1841." Ralston's Ancestors Ship's List
Find A Grave: Memorial #53435000 Find A Grave, database and images (https://www.findagrave.com : accessed 01 August 2018), memorial page for James Picken (1803–17 Aug 1888), Find A Grave Memorial no. 53435000, citing Scottish Cemetery, Caledonia, Boone County, Illinois, USA ; Maintained by Amelia Crombie-Christy (contributor 46861625) .
"United States Census, 1850," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M85H-WWB : 12 April 2016), James Picken, Harlem, Winnebago, Illinois, United States; citing family 73, NARA microfilm publication M432 (Washington, D.C.: National Archives and Records Administration, n.d.).