Have found a William and Ann in the right area but this means a) that Ann's age latterly is wrong, b) years married 1911 should be 62 (not 52) and c) second name of Elizabeth not used before 1901?
However, they appear to have had 12 children, 3 of whom died, all registered Stoke on Trent:
Annie birth Dec.1849
Thomas birth Dec.1851
Mary birth Dec.1853
Rachel birth Dec.1855
Eliza birth Dec.1857
Ellen birth Sept.1859
William birth Dec.1861
Charlotte birth Jun.1864, died March 1866
Charlotte birth Mar.1866, died 1869
Sarah Jane birth Sept.1867
Dorothy birth Mar.1869, died 1869
Julia birth Jun.1870
All show mmn as Robinson - William Shaw married Ann Robinson 17/6/1849 Stone, Staffordshire and all children shown born Longton, Staffordshire.
Looks like grandson Robert bc.1895 was illegitimate - Robert Machin Shaw birth Mar.1896 Stoke on Trent.
Annette