There is some confusion between the 2 different Ann Pearsalls – different generations.
Ann (nee Pearson) widow of William Pearshall
in 1841 census at Brierly Hill, with 2 sons
Ann Pearsall 70 Publican (she died in 1850)
William Pearsall 40 Boiler maker
James Pearsall 25 Boiler maker
The other Ann Pearsall was the widow of Joseph.
Both Anns were involved with running a public house, both are “your” Anns, but they are different generations.
Some of the records in your reply #14, refer to the older Ann Pearsall (who had a son named James), and some of it refers to the younger Ann. They do not all relate to the same Ann.