Charlotte's father, Bryan Edwards, refers to her as his daughter in his will, and in this (in 1800) he left her £2000. She was born in Jamaica 2 years before he returned to England in 1774.
Unlike other wills of white men I have read, who had similar 'relationships' (though we can rarely be sure whether the term 'relationship' accurately covers the nature of their unions) with women in Jamaica during this period, of whom there were many, in his will, Edwards never specified the ethnicity of Elizabeth Gaverick, later Nicolle; it was her illegitimacy that labelled her and she evidently carried the stigma of this to her grave - as indicated by the info you refer to on the NA website.
It is likely that she was of both white and black heritage, a combination that, over succeeding generations, depending who she had relationships with, may have resulted in her being an ostensibly black person with a paler skin tone or an ostensibly white person with a darker skin tone.
One such family I have looked at has produced children whose skins are pale but their heritage from Africa has produced decidedly wiry hair.
The Dix who Charlotte married was Edward Dix RN, and their son Edward appears to have married Martha Dix, who, as a daughter of the Rev Joshua Dix, was his cousin. This I assume is your line of descent, as Charlotte's daughter had no children.
thanks for your response