Hello Ruby
I don't know whether you have this or not, but here is Frederick in 1901. His middle name is James.
16 Wood St Swadlincote
William Dennis Head 48 Coal Miner Hewer Derby, Masham
Fanny " Wife 45 Stafford, Tamworth
John H. " Son 21 Sanitary Pipe Maker Swadlincote
William " Son 19 " " " Stafford, Tamworth
Emily " Daur 13 Gresley
FREDERICK JAMES " Son 10 "
Elsie May " Daur 9 "
Gertrude Nellie " " 7 "
Evalyn Maude " Daur 3 "
Francis Wm Eames Grandson 11 months "
RG13 Piece 2638 Folio 123 Page 20(Frederick and the later children have been transcribed in Ancestry as having the last name James not Dennis, but they are definitely Dennis)
In 1891 the family is Church Gresley together with James Hunter (transcribed as Hemker) - Fanny's father. William's age is transcribed as 57 and Fanny's as 56, but these are definitely wrong.
In answer to your original question, Mary definitely couldn't be Fred's daughter - he'd be too young in 1904. She could certainly be his sister. Fanny would be 48 so the biology would be possible

Isobel