Mary must have died between Q4 1851 (when Elizabeth born) and 1861 census when children are with other family members.
If born soon before 1817, then most likely the Sharples death.
LancashireBMD shows age at death and has few possible deaths for Mary Mather in Sharples (i.e. registered Bolton or Bury):
1) 1851, South Bury, aged 40
2) 1857, East Bolton, aged 53
3) 1858, Sharples, aged 33
4) 1858, East Bolton, aged 48
5) 1861, West Bolton, aged 55
6) 1862, Little Bolton, aged 56
Lancashire Death indexes for the years: 1851
MATHER Mary 40 Bury South BS/9/71
or
Lancashire Death indexes for the years: 1858
MATHER Mary 33 Sharples SH/4/493
or
Lancashire Death indexes for the years: 1857
MATHER Mary 53 Eastern Bolton EB/28/24
There are 6 different MATHER marrying Mary in Bolton 1844 to 1851, so the Sharples death is quite likely another.