1851 Fenny Stratford, Buckinghamshire John Shackleton Head 48 Labourer England Edith Shackleton Wife 44 Fenny Stratford, Bucks Francis Shackleton Son 15 Fenny Stratford, Bucks Ann Shackleton Dau 11 Plater Fenny Stratford, Bucks Elizabeth Shackleton Dau 7 Fenny Stratford, Bucks Mary Shackleton Dau 5 Fenny Stratford, Bucks Edith Shackleton Dau 4 Fenny Stratford, Bucks HO107/1723 Folio 141 Page 28.
In 1861 John Shackleton says that he is born in Fenny Stratford. I found a christening for a John Shackleton on IGI 8 Feb 1803 Fenny Stratford. Parents William and Ann http://www.familysearch.org/http://www.familysearch.org/
I think it is very unlikely that Mary is directly related to Ernest Shackleton. Ernest was born in Ireland where his family had lived for many years. His family was originally from Yorkshire and if there is a connection it would be a few generations back. See biog Ernest Shackleton: http://indigo.ie/~jshack/ernest.htmlhttp://indigo.ie/~jshack/ernest.html