John -
Have now had a chance to look in detail at the info you dug up, bits David found, and stuff I dug out myself and it seems to pan out like this:
Thomas Tatman, bap 27 Jul 1766, Blunham
Mary Crawley, bap 1 Jul 1770, Cople
Married: 6 Jan 1792, Northill - by licence
Children:
Mary Tatman, born 11 Feb 1792 (!), bap 15 May 1796, Cople
also possible: Thomas Tatman (or Crawley?), b about 1789, no baptism found, buried Cardington 19 Mar 1813 aged 24.
The marriage broke down - not surprisingly, as it seems to have been a shotgun wedding the the first place! They only just made it to the altar before Mary Jnr was born. By 1802, Mary Tatman is in Cople attempting to marry William Armstrong, a widower with existing family. Notably two sons, John and George. Her husband is living in Gt. Staughton.
A Thomas Tatman was buried in Lt Staughton on 13 Aug 1825, aged 59. (A perfect fit with the above baptism in Blunham).
Mary Tatman and William Armstrong had an illegitimate son, Henry, b 1803, who was baptised as an adult on 6 Dec 1826 in Cople.
They almost certainly also had an illegitimate daughter who was not baptised at all. Hannah, b 1806 in Cople, according to later census returns. There may have been a son as well, Samuel, born and buried in 1814, and others who have not yet surfaced.
Mary Tatman Jnr, daughter of Mary Snr and Thomas Tatman, married Joseph Hartop in Cople on 19 Jan 1817. One of her witnesses was her half-brother John Armstrong.
Henry Tatman Armstrong married Maria Cambers in Cople in 1826.
Hannah Armstrong married John Bassett in Cardington on 25 Dec 1827. One of her witnesses was Joseph Hartop, her half-brother-in-law. Joseph would have been her only male relative in the immediate area - her half-brothers John and George Armstrong had both moved away by then to Blunham and Eaton Socon.
William Armstrong was buried in Cople on 11 Feb 1828.
Mary Tatman moved to Cardington, to live with one or the other of her daughters. She died and was buried 26 Nov 1828 aged 57, a perfect fit with the above baptism for Mary Crawley in Cople.
Now, of course, it MIGHT not have been like that...but it all looks to be beyond any reasonable doubt...
Thanks very much, John and David, for helping me piece it together.
NB All IGI info is extractions - member entries (some highly spurious!) have been ignored.