Hello
My 4xG grandparents Thomas Carrington (1756-1827) and Jane Foulkes (1759-1847) were the parents of Anne Carrington. Anne was baptised at Llanarmon-yn-Ial, Denbighshire in 1802. My connection was one of her older brothers John Carrington (b1795)
Thomas died in 1827 but Jane lived on until 1847. Jane does appear on the 1841 census of Llandegla, living with another son, Aaron and his family. Thomas left a will, available on the NLW site - SA\1828. He left daughter Ann(e) ten pounds - possibly she was still single in 1827. Anne's older sisters were already married. Alice (1794-1876) married a David Cadwaladr and Ellinor (Ellen - 1791-1855) married a William Hooson in 1820.
Have you tried the Minera history site for information on Anne's marriage to John Williams?
Hope this helps
Heather