According to the Visitations of Shropshire (Charlton of Apley pedigree, p. 101), her father was Piers Stanley of Flintshire.
Wikipedia has this to say about Thomas Stanley, 2nd Earl of Derby:
Marriage and issue
Derby was betrothed in 1498 to Elizabeth Wells, the daughter of John Welles, 1st Viscount Welles, by Cecily of York, the daughter of King Edward IV and Elizabeth Woodville. A papal dispensation was obtained for the marriage. However Cecily died that year. By indenture dated 17 December 1505 Derby married Anne Hastings, the daughter of Edward Hastings, 2nd Baron Hastings, and Mary Hungerford, and by her had two sons and a daughter:[6]
* Edward Stanley, 3rd Earl of Derby
* Margaret Stanley (d. shortly after January 1534), who married Robert Radcliffe, 1st Earl of Sussex, and by him had two daughters, Jane, who married Anthony Browne, 1st Viscount Montague, and Anne, who married Thomas Wharton, 2nd Baron Wharton.
* John Stanley (died young).[citation needed]
Source cited for the first two children is Richardson, Douglas (2011). Magna Carta Ancestry: A Study in Colonial and Medieval Families, ed. Kimball G. Everingham IV (2nd ed.). Salt Lake City. ISBN 1460992709
Please note that there is no daughter Anne.
From https://histfam.familysearch.org//getperson.php?personID=I72123&...
Notes
(Research):KINSHIP: Conflict/Error> J-Morris' 'Shropshire Genealogies' volume 4 page 1977 makes her the daughter of Pirs Stanley who was married to Jonet daughter of John Parker, an inserted generation not found the base pedigree.
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