The following Hardings were all the children of William and Harriet and baptised within 100 miles from Warwickshire:

Name                        Bapt date          Bapt Place                         Birth date

William Harding            12 Mar 1786        Britwell Salome, Oxon
Hannah Harding             30 Sep 1787        Britwell Salome, Oxon
John Harding                9 Aug 1789        Britwell Salome, Oxon
Harriet Maria Harding      30 May 1790        St Edmund, West Kingsdown, Kent    
Catharine Harding          10 Nov 1791        Hampton Lucy, Warks
Charles Harding            10 Nov 1792        Hampton Lucy, Warks
Charles Harding            14 Sep 1793        Hampton Lucy, Warks
Henry Harding               2 Nov 1794        Hampton Lucy, Warks
John Harding               17 Nov 1795        Hampton Lucy, Warks
Harriet Harding            21 Nov 1796        Hampton Lucy, Warks
Elizabeth Octavia Harding   9 Apr 1798        Hampton Lucy, Warks
Francis Harding             8 Aug 1800        Hampton Lucy, Warks                 28 Apr 1799
Jane Harding               20 Oct 1801        Alveston, Warks                     27 Sep 1801
Edward Harding             23 Feb 1803        Alveston, Warks                     22 Nov 1802
Edward Harding             13 Sep 1804        Alveston, Warks
Sophia Harding             19 Jan 1908        Alveston, Warks
Sophia Harding             23 Jun 1810        Alveston, Warks

These all look like being members of the one family, though with a house move around 1801.

From the will of Henry Harding it seems that his eldest brother was in fact named William Judd Harding.  It sounds as if William Judd was shildless or son-less and that the next brothers, John, Charles and Charles had all died or also had no children as Henry harding was expecting his son William to inherit Baraset, which he did but then sold (because he could not afford to run it?).

Additionally there was a Charles born in 1812 in London to a William-Davis and Harriet Harding and an unnamed child in 1813 in Gloucester but to William and Harriet Harding.

25 years of child rearing.

From the repeated use of some of the forenames, it looks like there were a few infant deaths for John, Charles, Harriet, Edward, and Sophia.  These are more difficult to nail down as Harding is relatively common as a surname so I searched on in the above baptism locations plus five miles around, but no such deaths could be found.
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He is reported to have been of Baraset, Alveston, Warks and certain this address appears in records for his descendants.  Assuming this was correct for him this make it far easier to identify his birth family.

Further his father is said to have been Judd Harding.  From this there are two births of William Hardings with a father of Judd Harding:

Bapt date         Bapt place                        Mother's forename

14 Apr 1754       Deritend and Bordesley, Warks     Sarah
22 Feb 1759       Tanworth in Arden, Warks          Elizabeth

So: Did Judd have two marriages?

Not that I can see: there was one, his father's?, in 1724 to Rebecca Townsend and another in 1753 to Elizabeth Hunt.  Judd might still have been the father of the first William.  There was only one Judd baptism from 1715 to 1735, and that was on 17 Mar 1726 and his father was another Judd, very probably the man who married in 1724.
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Assuming that Elizsbeth was the wife of Judd and the mother of William who married Harriet Sweedland, the siblings of Judd can be located.  They are listed in the Notes for William's presumed father, Judd.
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From "A copy of the Register of Marriages, Baptisms and Burials for the Town of Calcutta in Bengal during the year of our Lord 1784:

November 1784
...
7th(?) Mr William Harding Factor in the honble company's Service  & Miss Harriet Sweedland.

(transcribed by me from a somewhat illegible image of a register.)
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