George re-married in 1865 to Edith Burton (nee Waters?) Could this Edith have been related to Edith Waters who was married George's father
Possibly (probably?).
It looks like Edith, who married George Kidman (jnr) in 1865, was the daughter of Thomas and Ann Waters and her first husband was William Burton, who died in 1857.
GRO BMD references:
1847 Q2 Marriage: William Burton and Edith Waters; Biggleswade; 06; 73
1848 Q2 Birth: Thomas Waters Burton (mmn: Waters); Biggleswade; 06; 37
1857 Q2 Death: William Burton; 37 (est b1820); Biggleswade; 03b; 218
Edith's parents:
1851 Q4 Death: Ann Waters; 46 (est b1805); Biggleswade; 06; 40
1863 Q4 Death: Thomas Waters; 69 (est b1794); Biggleswade; 03b; 233
Baptism:
name: Edith Waters
baptised: 14 May 1826; St Mary Magdelane, Dunton
father: Thomas, yeoman
mother: Ann
Marriage:
married: 13 Apr 1847; Dunton
groom: Thomas Burton
bride: Ann Waters
grooms father: Thomas Burton
brides father: Thomas Waters
https://familysearch.org/ark:/61903/1:1:NVS1-8TCMarriage:
married: 13 Apr 1847; Dunton
groom: George Kidman
bride: Ann Burton
grooms father: George Kidman
brides father: Thomas Waters
https://familysearch.org/ark:/61903/1:1:NVSB-8XXCensuses:
1841 Newton Bury
Edith (presumably) with her parents Thomas and Ann
Ref HO107; Piece 2; Book 14; Folio 3; Page 2;
1851 Dunton Newton
Thomas and Ann Waters with various children (but not Edith)
Ref HO107; Piece 1753; Folio 294; Page 1;
1851 Biggleswade
Edith with first husband William Burton and son Thomas, and Edith's sister Mary
Ref HO107; Piece 1753; Folio 573; Page 42;
1861 Newton Bay Farm, Dunton
Edith, widow, living with her widowed father Thomas
Ref RG09; Piece 995; Folio 125; Page 16;
Probate index for Edith's father:
Thomas Waters
10 Mar 1864
The will of Thomas Waters late of Newton Bury in the parish of Dunton in the county of Bedford Gentleman deceased who died 1 December 1863 at Newton Bury aforesaid was proved at the Principal Registry by the oaths of John William Ryder of Ramerwick Manor House in the parish of Ickleford in the county of Hertford Farmer and Waters Masters of Wrestlingworth in the said county of Bedford Farmer two of the Executors.
Effects under £3,000
No: 213
https://probatesearch.service.gov.uk/Calendar?surname=Waters&yearOfDeath=1864&page=5#calendarFrom the censuses Edith's father Thomas was born c1793 in Eyeworth, which tallies with a baptism record:
Baptism:
name: Thomas Waters
baptised: 17 Nov 1794; All Saints, Eyeworth
father: Thomas
mother: Mary
Looking at Edith who married George Kidman (snr) in 1822, from the censuses she was born c1801 in Edworth or Dunton. The Beds FHS surname index has only one baptism for an Edith Waters around this time and that's in Eyeworth:
Baptism:
name: Edith Waters
baptised: 28 May 1802; All Saints, Eyeworth
father: Thomas
mother: Mary
age: 2 years
So I think it's quite likely that the older Edith is the aunt of the younger Edith.
There is another possible connection between the Kidmans and Waters, which may just be a coincidence. I had previously come across a (very long) newspaper article re. the death of a Bethia Donne in April 1874. Bethia was named as the daughter of George Kidman, a farmer of Edworth. Bethia's body was found in the River Ouse at Bedford and various witnesses stated that they knew her and that she was the daughter of George and that she'd been married to George Waters and Charles John Donne, of London, and that Bethia had separated from Charles (after he'd brought another woman home).
The coroner reached the verdict of "found drowned" but the witness statements give the impression it may have been a suicide.
Bethia's possessions included included a mourning card, "Sacred to the memory of George Kidman, of Edworth, Beds, died Sep 1st, 1864, aged 66 years", so I think its safe to say she was the daughter of George (snr) and Edith.
Looking at the marriage of Bethia and George Waters, George names his father as Thomas (coincidence?).
Marriage:
married: 03 Mar 1866; St Pancras parish chapel; lic
groom: George Waters; fa; bach; gardener; St Pancras
bride: Bithia Kidman; fa; spin; -; Edworth, Bedfordshire
grooms father: Thomas Waters (dec)
brides father: George Kidman (dec)
witnesses: Joseph Lautre? Roberts, Wm? Buck??ge
GRO BMD references:
1866 Q1 Marriage: Bithia Kidman and George Waters; Pancras; 01b; 135
1872 Q2 Marriage: Bethia Waters and Charles John Doune; Pancras; 01b; 280
1874 Q2 Death: Bethiah Donne; 36 (est b1838); Bedford; 03b; 197