Hello Gaie,
I think I have traced Susanna's mother.
I believe she is Ann Wilson who was born at Bexhill in abt 1813 and married William Carpenter at Hollington on 23 August 1831. Ann had 3 children, Henry (abt 1837), Mary (abt 1839 and Susanna (abt 1841). So Susanna's birth name was Carpenter, although she changed it in later years.
William Carpenter died in 1843 and Ann remarried William Ashdown between 1843 and 1851. They had three more children, Alfred (abt 1851), George (abt 1855 and Edward (abt 1857). Phew!!
I guess it is still possible that William Ashdown is the son of William and Susan Beany but I have no corroboration yet.
Sorry to go on a bit but I thought you might find some of it interesting?
Regards
Graham