Could you give us a census reference for Mary after her marriage to William please? At the moment I can't see a Mary McCormick who matches your details.
On the earlier censuses there is a Mary Wright born c1849 in Denton/Haughton Green whose parents seem to be William and Mary:
1851
HO107/2235/171/15 - Haughton Green, Lancashire
William WRIGHT Head 46 Works in a Coal Pit b. Haughton
Mary WRIGHT Wife 45 b. Stockport
Jane WRIGHT Dau 18 Frame Tenter, Cotton b. Haughton
Eliza WRIGHT Dau 17 Frame Tenter, Cotton b. Haughton
William WRIGHT Son 12 Frame Tenter, Cotton b. Haughton
Betty WRIGHT Dau 10 Frame Tenter, Cotton b. Haughton
George WRIGHT Son 7 Scholar b. Haughton
David WRIGHT Son 4 b. Haughton
Mary WRIGHT Dau 1 b. Haughton
(In 1861, William is married to a second wife, Sarah, and only the three youngest children are still at home.)
Rambler