I think this might be your family in 1851:
HO107/1751 folio 33A
Brook End Rd., Keysoe
William Barnard head marr 50 ag lab b Keysoe
Ann Barnard wife 50 b Keysoe
Richard Barnard son unm 22 ag lab b Keysoe
John Barnard son unm 20 ag lab b Keysoe
Sharlott Barnard dau unm 17 lace maker b Keysoe
James Barnard son 15 ag lab b Keysoe
Charles Barnard son 12 ag lab b Keysoe
Elizabeth Barnard dau 9 b Keysoe
Eliza Barnard dau 2 b Keysoe
Looking at 1861 I'm sure they're your family
RG9/985 folio 43A
Brook End Keysoe
Ann Barnett head widow 61 lace maker b Keysoe
William Barnett son unm 37 ag lab b Keysoe
Elizabeth Barnett dau 19 lace maker b Keysoe
Eliza Barnett dau 12 lace maker b Keysoe
William's age is spot on for him to have been the illegitimate male son who gave rise to the Filiation Order in 1824.
And in 1841 indexed as Barnes, and the final letter could either be an s or a t without the bar.
Brook End Keysoe
William Barnet 40 ag lab
Ann Barnet 41
William Barnet 18
Richard Barnet 14
John Barnet 11
Sharlot Barnet 9
James Barnet 6
Charles Barnet 3
same house, separate family unit
William Barnard 20 ag lab
All born in Beds
So William Barnett died some time between 1851 and 1859.
Coincidentally (and I don't believe in coincidences) there was another Barnett, William, also living in Hargrave in 1861, born in Gt Barford, Beds. I wonder if there's a connection between the Keysoe Barnetts and the Gt Barford family.
So going back to your original query I think David was the son of Susannah Sturges who subsequently married Joseph Eartherds on 6 Feb 1826. Susannah and your Ann may have been sisters but it would take more work to prove this as neither was baptised in the established church, at least not in Beds.
There's a burial at Keysoe of Susanna Ethards aged 35 on 12 July 1832 and in 1851
HO107/1751 folio 36B
Joseph Edwards head widower 51 ag lab b Sharnbrook Beds
Elizabeth Edwards dau 21 lace maker b Keysoe
On the IGI there is a baptism of Eliza Ethards on 14 Oct 1827, daughter of Joseph and Susanna, and I suspect that Edwards/Ethards may be the same people. No sign of David Sturges though - I can't see a David born Keysoe that fits in any census, nor is there a burial in Keysoe, or anywhere else in Beds 1826-46. He seems to disappear.
Regards
David