The 2nd marriage referred to, to a Sarah Pidcock with no actual year is not the right one.
As birth of youngest child Sarah shows mmn as Bolsover this must be Thomas' second marriage:
Thomas Welton, widower, married Sarah Boulsover, spinster, 15/6/1824 Manchester. Thomas' actual signature looks like Wetten.
I think the birthplace of Sarah on 1851 census - which is so unclear - is supposed to be Eckington, Derbyshire and that her baptism must be either Sarah Bolsover bp.5/11/1797 Eckington, dau. of John and Elizabeth or Sarah Bolsover bp.7/1/1798 Eckington, dau. Thomas and Mary.
Thomas Wetton, shown to be born in Ashbourne, must be the one baptised 16/1/1788 Ashbourne, son of William and Mary (as has been mentioned).
He was buried, aged 68, 3/12/1854 Chorlton upon Medlock and transcribed as Thomas Welton but looking at original record is probably Wetton.
Annette