I could not find any references in the Shackleton book to your William Shackleton or to Elizabeth Rothwell.
However, following the publication of the book in 1972, there were periodic updates in the form of Newsletters which included letters received by the author with additional information.
One letter was from a Betty sending information about her ancestress, Ann A.Shackleton Evans b 1818 at Staffordshire, England; d 1860-1870? Ionia Co Michigan. Ann was the daughter of Alexander Shackleton and Elizabeth Rothwell.She also comments that a distant cousin, Alice,in Belgrave, Ontario, has written a family history.Alice says that the family originated in Yorkshire rather than Staffordshire. Bettysays that Ann had a brother, Matthew and that she does have some dates.
Betty wrote to Harry, another distant cousin in Goderich, Ontario, about the Shackleton book. In his letter to the author as printed in the Newsletter he says , "My great grandfather, William Shackleton came to Canada with his family in 1826. I believe he came from around where Crewe now is in Cheshire. I have been told that a cousin of mine, who was raised by my grandfather that he said that our great grandfather had been disinherited for marrying a servant girl. I have cousins in Alyoma, more in Alberta, another in Detroit, and a nephew in Ottawa. There are more Shackletons around Aylmer, Ont.....The spell the name with the "e" before the "l", others the reverse, but they are all related. He said that three brothers came out from Yorkshire around 1850."
I would be glad to copy the pages of the newsletter with this information if you would send me your mailing address by e-mail. Or if you just want the names and addresses (as of 1975, when they were written), send me your email.