After you have the M/C I think you will find her Father was Richard;
1861 Census
Ingram, Northumberland
Richd Rutherford, 40, Head, Mar, Shepherd, born Elsdon, Northumberland
Isabella Rutherford, 40, Wife, Mar, born Scotland
Margaret Rutherford, 15, Daug
John Rutherford, 12, Son, born Scotland
William Rutherford, 8, Son, Scholar, born Ingram
Janet Robinson, 42, Visitor, Widow
Ralph Dunn, 25, Servant, Shepherd
Alex Hindmarsh, 24, Servant, Shepherd
ISABELLA Rutherford age 10, born c 1851 Scotland, is in Glanton, Northumberland, visiting Alexander and Jane Hindmarsh.
1851 Census
East Hyndhope,
Oxnam, Roxburghshire, Scotland
Richd Rutherford, 30, Head, Shepherd, born northumberland,england, Elsdon
Isabella Rutherford, 33, Wife, born Newcastleton, RoxburghshireWife
John Rutherford, 2, Son, born Newcastleton
Christian Rutherford, 3mths, Daug, born Oxnam
Daug Margaret born 1846 from 1861 Census is not at Home in 1851 but is possibly visiting in Northumberland in 1851 Census.
F/S has Christians christening 1851 and FreeREG has her Parents Marriage 1842 In Roxburghshire.
To confirm everything;
Birth Reg GRO Index
RUTHERFORD, WILLIAM, Mothers mn AMOS
GRO Reference: 1853 M Quarter in GLENDALE Volume 10B Page 285
Burial;
William Rutherford
Death Date: 12 Apr 1863
Cemetery: Ingram, St Michael and All Angels Church
Parents Richard/Isabella
GRO has him as age 10