I'm going to research Charlotte Piggot/Pigot/Pygot's ancestry now, to see if a Richard Hague/Haigh appears anywhere - to see if the questions asked about the children's families at their baptisms were misunderstood.
Starting with Charlotte Piggot, bap 6th April 1763 at Conisbrough, daughter of William 'Pygot' and his wife Anne.
It appears that Charlotte may have had these siblings, although there may be more than one William Pigot here, as some baptisms are at Conisbrough (where Charlotte was baptised) and others are nearby at Doncaster.
- Wm 'Pigot' bap 4 July 1756 in Conisbrough.
- Elizabeth 'Pygot' bap 6 April 1763, Conisbrough.
- Sarah 'Pyegot' bap 24th February 1760, Conisbrough.
- Hollis Robert 'Pigot' bap 10 April 1758, Doncaster.
- Elizabeth 'Pygot', bap 9th April 1759, Doncaster.
- Wm Brooke 'Pigot', bap 27th February 1757, Doncaster.
- Wm 'Pigot' bap 24th March 1760, Doncaster.
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EDIT: It looks like there were two William Piggot's - one at Doncaster and one at Conisbrough/Wadworth by Doncaster.
- William 'PYKIT' (aged 28) m. Anne Bolton (aged 21), 12th or 13th July 1755, St Mary's, Wadworth. Both of Wadworth, by license. Witnesses: John Guest and Emmanuel Martin.
- William 'PIGOT' m. Eliz. Brooke, 20th April 1756, St George's, Doncaster.
So since Charlotte Pigot's parents were William and Anne, this seems to match with the first marriage - between William 'Pykit' and Anne Bolton, in 1755, 8 years before Charlotte's baptism.
So it appears that the Conisbrough baptisms belong to this couple, and the Doncaster baptisms likely belong to another William Pigot and his wife Elizabeth Brooke.
So this leaves in my family:
William Pygot, who married Anne Bolton of Wadworth on 13th July 1755, St Mary's, Wadworth.
And the couple had the following children; William (bap 4 July 1756), Sarah (bap 24th Feb 1760), Elizabeth (bap 6 April 1763), and Charlotte (bap 6 April 1763).
I can't find a possible baptism for Wm Pygot, but there are two possibilities for Anne Bolton. She was born about 1734 as she was 21 at her marriage to Wm in 1755.
- Anne Bolton, daughter of Richard Bolton. Bap 9 Jul 1735 at Conisbrough.
- Anne Bolton, daughter of Thomas Bolton. Bap 22 Apr 1733 at Conisbrough.