I am also researching ADAMS in Staffordshire. My family were almost all potters from around Stoke upon Trent. I do not have any connection to your enquiry but have looked up the following on the mormon website "Family Search" for you. Thomas Adams married Elizabeth Buxtones on 14 February 1792 at All Saints, Dilhorn, STS. They appear to have had children as follows: - James Adams christened 10 Mar 1793 at Cheadle (ties up with marriage date!) Thomas Adams Christened 28 December 1794 at Cheadle Mary Adams Christened 27 June 1797 at Cheadle Ellen Adams Christened 17 February 1799 at Cheadle Sarah Adams Christened 20 July 1800 at Cheadle George Adams Christened 27 January 1805 at Cheadle Charlotte Adams Christened 16 May 1807 at Cheadle
There may be more but these are all I noted.
George Adams married Charlotte Thorley 1 February 1830 at Fulford, STS.