Geraldo,
To make up for going completly off track before, I think I've found them on the 1911 census, but it's not as Emily Taylor:
Highfield, Westmeon, Petersfield, Hants
Joseph Mills, Head .Married M 60 b. 1851 Dairy Preston Candover Hants: Farmer
Harriet Mills, Wife. Married 38 years F 63 b. 1848 Old Alresford Hants
Emily Martha Mills, Daughter Single F 30 b. 1881 Preston Candover Hants: Dairy
Ernest Daniel Mills, Son Single M 23 b.1888 Exton Hants Work On Farm
Gwendoline May Parker, Granddaughter F 11 b. 1900 Exton Hants
Gwendoline May Mills, Granddaughter F 3 b. 1908 Simons Town S Africa
The reference to follow this up is RG14PN6155 RG78PN287 RD104 SD2 ED5 SN165
If following this up please be aware that in the site I used to search BOTH Gwendoline Mays have been transcribed as Parker, but on the original document your mother's surname is clearly written as Mills. Gwendoline May must mean something to the family to have two granddaughters both christened the same (unless Emily was homesick in SA and decided to name your mother after her cousin)
Emily is single, certainly isn't using the name Taylor, and that is entirely understandable given your family story. You may wish to follow this up and look at the certificate yourself, I think you'd find it worthwhile because although there's nothing else on it I haven't written here I think that just seeing the 1911 images in what must be your great-grandfather's own hand is always special. Good luck