Her death:

First name(s) EMILY
Last name HARDING
Gender Female
Birth year 1797
Age 86
Death quarter 4
Death year 1883
District STRATFORD ON AVON
County Warwickshire
Volume 6D
Page 365
Country England
Record set England & Wales deaths 1837-2007
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These children are found on the baptism files on FindMyPast:

Last name  First name(s)  Year Of Birth  Year Of Death  Year  Record set  Location
Harding William Feilding 1829 — 1829 England Births & Baptisms 1538-1975  Aldridge, Staffordshire
Harding William Feilding 1829 — 1829 Staffordshire Baptisms  Aldridge, St Mary the Virgin, Staffordshire
Harding William Feilding — — 1829 England Births & Baptisms 1538-1975  Aldridge, Staffordshire
Harding Emily Jane — — 1833 England Births & Baptisms 1538-1975  Aldridge, Staffordshire
Harding Emily Jane — — 1833 England Births & Baptisms 1538-1975  Aldridge, Staffordshire
Harding Emily Jane — — 1833 Staffordshire Baptisms  Aldridge, St Mary the Virgin, Staffordshire
Harding Charles Henry — — 1835 England Births & Baptisms 1538-1975   Aldridge, Staffordshire
Harding Charles Henry — — 1835 England Births & Baptisms 1538-1975  Aldridge, Staffordshire
Harding Charles Henry — — 1835 Staffordshire Baptisms  Aldridge, St Mary the Virgin, Staffordshire
Harding Caroline Gertrude — — 1838 England Births & Baptisms 1538-1975  Aldridge, Staffordshire
Harding Caroline Gertrude — — 1838 England Births & Baptisms 1538-1975  Aldridge, Staffordshire
Harding Caroline Gertrude — — 1838 Staffordshire Baptisms  Aldridge, St Mary the Virgin, Staffordshire

This looks like four children.  The Staffordshire Baptism records have an image of the record, so I will be downloading and using those.
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The 1841 census shows an eldest daughter born outside Staffs plus a second eldes dau. Georgiana born in Staffs, and they all, apart from William Feilding H, were living at the Rectory, Aldridge, Staffs:

First name(s)  Last name  Sex  Age  Birth year  Birth place
Henry      Harding  Male    45  1796  -
Emily      Harding  Female  40  1801  -
Catharine  Harding  Female  12  1829  -
Georgiana  Harding  Female  10  1831  Staffordshire, England
Emily      Harding  Female   8  1833  Staffordshire, England
Caroline   Harding  Female   3  1838  Staffordshire, England
Emma       Still    Female  25  1816  -
Joseph     Childs   Male    25  1816  -
Mary       Palmer   Female  55  1786  -
Mary       Leigh    Female  18  1823  -
Mary       Briscoe  Female  16  1825  -
Sarah      Briscoe  Female  18  1823  -
Elizabeth  Hooper   Female  25  1816  -

Ref:
Archive reference  HO107
Piece number       977
Book number        1
Folio number       11
Page number        14
Combined:          HO107, place 977, book, 1, folio 11, p. 14
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In 1851 Henry had moved (promoted?) to vicar of Shalford (or Stratford?) upon Avon, living in College lane, Old Stratford and they only had two of their children with them, though the four family members required six live-in servants to cater for their needs:

First name(s)  Last name  Relationship  Marital status  Sex  Age  Birth year  Occupation  Birth place
Henry      Harding   Head      Married    Male    56  1795  Vicar Of Stratford Upon Avon  Hampton Lucy, Warwickshire, England
Emily      Harding   Wife      Married    Female  53  1798  -  Shropshire
Georgina E Harding   Daughter  Unmarried  Female  19  1832  -  Aldridge, Staffordshire
Emily J    Harding   Daughter  Unmarried  Female  18  1833  -  Aldridge, Staffordshire
William    Hill      Servant   Married    Male    37  1814  Butler  Willerby, Shropshire
Elizabeth  Parry     Servant   Unmarried  Female  26  1825  Ladies Maid  Bicton, Shropshire
Martha     Lewis     Servant   Unmarried  Female  23  1828  House Maid  Montford, Shropshire
Emma       Jones     Servant   Unmarried  Female  18  1833  Kitchen Maid  Baschurch, Shropshire
Harriett   Pinfold   Servant   Unmarried  Female  21  1830  Ladies Maid  Alverton, Warwickshire
Elizabeth  Williams  Servant   Unmarried  Female  33  1818  House Keeper  Wales

Ref:
Archive reference  HO107
Piece number       2074
Folio              517
Page               18
Combined           HO107, piece 2074, folio 517, p. 18
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By 1861 they had left Aldridge and were living in some style in Hampton Lucy with only Emily Jane and William with them. As Henry was born in Hampton Lucy I wonder if he had inherited his parents house:

First name(s)  Last name  Relationship  Marital status  Sex  Age  Birth year  Occupation  Birth place
Henry        Harding   Head      Married    Male    65  1796  Clergymen  Hampton Lucy, Warwickshire
Lady Emily   Harding   Wife      Married    Female  63  1798  -  Shropshire
William      Harding   Son       Unmarried  Male    31  1830  Royal Navy  Aldridge, Staffordshire
Emily Jane   Harding   Daughter  Unmarried  Female  28  1833  -  Aldridge, Staffordshire
William      Jones     Servant   Unmarried  Male    34  1827  Butler  Shrewsbury, Shropshire
James        Leake     Servant   Unmarried  Male    30  1831  Groom  Baschurch, Shropshire
Elizabeth    Davies    Servant   Widow      Female  50  1811  Cook  Pontesbury, Shropshire
Mary         Kirkland  Servant   Unmarried  Female  45  1816  Ladiesmaid  Kingham, Gloucestershire
Elizabeth    Kirkland  Servant   Unmarried  Female  27  1834  Housemaid  Flintshire, Wales
Mary         Davies    Servant   Unmarried  Female  18  1843  Kitchen Maid  Bettws

Ref:
Archive reference  RG09
Piece number       1862
Folio              60
Page               1
Combined           RG09, piece 1862, folio 60, p. 1
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In 1871 she was widowed and had two daughters with her at Elm Hurse lane, Old Stratford, the first widowed too but given her maiden name only:

Note: The above assertions about Catherine Frances may be not wholly correct in view of the now total mystery of her supposed marriage.

First name(s)  Last name  Relationship  Marital status  Sex  Age  Birth year  Occupation  Birth place
Emily       Harding Head      Wid Female  73  1798  Annuity  Berwick House, Shropshire
Cather F    Harding Daughter  Wid Female  42  1829  Annuity  Bainack, Stanford
Emily Jane  Harding Daughter  Unm Female  38  1833  Annuity  Staffordshire, Aldridge
Elizabeth   Williams  Servant   Unm Female  64  1807  House keeper  Wales
Fanny       Willetts  Servant   Unm   Female  36  1835  Ladies Maid  Yorkshire
Mary        Smith    Servant    Unm   Female  20  1851  House maid  Warwickshire
Elizabeth   Mills    Servant    Unm   Female  24  1847  Parlour maid  Worcestershire, Nun Blockley

Ref:
Archive reference  RG10
Piece number       3208
Folio              73
Page               30
Combined           RG10, piece 3208, folio 73, p. 30
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In 1881 she was still at Elmhurst and now had three of her daughters with her, one married, one a widow and one unmarried plus some grandchildren.  And it gives the correct married names of those two duaghters:

First name(s)  Last name  Relationship  Marital status  Sex  Age  Birth year  Occupation  Birth place
Emily        Harding    Head            Widow    Female  83  1798  Earls Daughter  St Mary's, Shropshire
Emily Jane Harding    Daughter        Single   Female  48  1833  -  Aldridge, Staffordshire, England
Catherine    Croker     Daughter        Widow    Female  52  1829  -  Lincolnshire, England
Amelia H     Croker     Grand Daughter  Single   Female  21  1860  -  Leamington, Warwickshire, England
Caroline G   de Winter  Daughter        Married  Female  43  1838  -  Aldridge, Staffordshire, England
Arthur H     de Winter  Grand Son       Single   Male    16  1865  Bankers Clerk  Brecknockshire, Wales
Harriet      Bourton    Servant         Single   Female  33  1848  Cook (Dom)  Hampton on the Hill, Warks
Lucretia     Clarke     Servant         Single   Female  26  1855  Housemaid  Harpole, Northamptonshire
Alice M      Cox        Servant         Single   Female  22  1859  Ladys Maid  City of London, Middlesex
John Parker  Howe       Servant         Single   Male    28  1853  Butler (Dom)  Clifton, Oxfordshire

Ref:
Archive reference  RG11
Piece number       3103
Folio              42
Page               10
Combined           RG11 piece 3103, folio 42, p. 10
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Her probate index:

The Honourable (commonly called Lady)
HARDING Emily
Personal Estate £9,500 11s. 6.
Resworn November 1884 £10 564 2s. 6d.
1 December [1883]  The Will with a codicil of the Honourable (commonly called Lady) Emily Harding late of Elmhurst Stratfor-upon-Avon in the County of Warwick Widow who died 8 October 1883 at Elmhurst was proved at the Principal Registry by Emily Harding of Elmhurst Spinster the Daughter and William Feilding Harding of Coverdale Lodge Leamington in said County Esquire the Son the Executors.
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In her will dated 13th August 1863 and in her codicil dated 9th January 1880 she mentioned:

Her late husband Rev Henry harding Rector of Stapleton, Shropshire, Clerk,
Her daughter Catherine Frances now the wife of Rev Thomas Burrowes Adams,
Her daughter Caroline Gertrude now the wife of Henry de Winton,
Her son William Feilding Harding,
Her daughter Emily Harding,
Her grandchild and god-daughter Mary Gertrude de Winton,
Her grandson Francis Henry de Winton,
Her grandson Richard Capel de Winton,

and in her codicil of :

Her daughter Catherine Frances Adams no the wife of Captain Richard Croker,
Her deceased daughter Georgina Harding,
Her (late?) brother Rev Everard Robert Bruce Feilding,
Her (late?) sister in law Mrs Anne Feilding.
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Their marriage from FamilySearch:

Name Henry Harding
Spouse's Name Emily Fielding
Event Date 11 Oct 1827
Event Place Monks Kirby,Warwick
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