Hi Chris,
I think you're right about a second marriage though the parish register itself is inconclusive. It doesn't say whether she was a widow or not, but I think the name of their second child more or less gives it away.
Thomas Cook & Sarah Cook both of this Parish were Married in this Church by Banns the 5th Day of October 1809 By me H. Houson Parish Vicar
This Marriage was solemnized between us Thomas Cook X his mark
Sarah Cook
In the presence of R. Sanders
Edwd. MillerSouthwell baptisms - Children of Thomas & Sarah Cook:
31 Mar 1810 - Elizabeth
31 May 1811 - Robert Barlow
22 Mar 1813 - Ann
28 Jun 1814 - Henry
13 Dec 1815 - Thomas
20 Jan 1818 - Jemima
27 Oct 1819 - William
28 Oct 1820 - Edward
8 May 1822 - James
Thomas was a "Blacksmith" on Ann's baptism and a "Stockingmaker" on all the rest.
Sarah's age on the censuses and death is about perfect for the Sarah "Sandiforth" (bap 1782) whom I assume you are searching for.
1841 census: Maythorn Cottage, Southwell, Notts (HO107/867, book 12, f 33, p 2)
Thomas Cook, 50, Stocking M, Y
Sarah Cook, 55, Y
Henry Cook, 25, Stocking Maker, Y
Thomas Cook, 25, Ag Lab, Y
Jemimah Cook, 20, Y
William Cook, 20, Ag Lab, Y
1851 census: King St, Southwell, Notts (HO107/2134, f 362, p 2)
Thomas Cooke, Head, Mar, 62, Frame work Knitter, Nottinghamshire Southwell
Sarah Cooke, Wife, Mar, 68, Nottinghamshire Southwell
Henry Cooke, Son, U, 36, Frame work Knitter, Nottinghamshire Southwell
Thomas Cooke, Son, U, 35, Agricultural Lab, Nottinghamshire Southwell
William Cooke, Son, U, 31, Agricultural Lab, Nottinghamshire Southwell
Sarah was buried at the Southwell Minster on 7 Jul 1858 (age 74), and Thomas on 1 Jul 1876 (age 88).
Thomas remarried after Sarah's death - you can find him on the 1861/71 censuses. His second marriage:
Southwell Minster - 10 Oct 1863 by Banns
Thomas Cooke, full age, Widower, F.W.K., of Southwell, father: William Cooke, Labourer
Rebecca Wells, full age, Widow, of Southwell, father: Henry Revill, Labourer
Signed: Thomas Cook (X his mark), Rebecca Wells (X her mark)
Witnesses: George Cook, Hannah Cook (X her mark)
I could prattle on all day about the Cooks, but I think I'll leave it there for now.

Alexander