I'm concerned re. parentage of Edith Adelaide Kaye too - a) there is no birth entry for anyone of this name born to James Kaye and Harriet Ninnim nee Butler and b) she does not appear on the census with family at all.
However, I wonder if there has been some confusion along the way. I note that an Edith Adelaide Kaye was born in 1874 in Eltham, Victoria to a James Kaye and Harriet Pearce.
She married a man surnamed Rojo in 1890 Victoria. Her death entry in 1954 Hawthorn, Victoria shows her parents as James Kaye and Harriet unknown.
Is this the Edith Adelaide Kaye you mean? If so, she was born in Australia, certainly wasn't a sister of Hannah and her parents were a different James Kaye and wife Harriet Pearce - this couple married in England in June quarter 1860 St. Columb, Cornwall and the 2 of them are living in St. Enoder, Cornwall in 1861 where both are said to have been born ca.1841. Harriet must have been about to give birth as a son William Albert birth in June quarter 1861 St. Columb, Cornwall. By 1864 the family were in Australia where the following born in Victoria:
John Thomas b.1864
Mary Ellen b.1866
Louisa Ann b.1869
Richard James b.1871
Edith Adelaide b.1874 (married a Rojo in 1890 Victoria).
So, to conclude, if the Edith Adelaide Kaye you refer to is the one who married a Rojo 1890 Victoria then she was definitely not a sister of Hannah. Edith born in Australia 1874, her parents being a James Kaye and Harriet Pearce who were both born (and married) in Cornwall and emigrated to Australia 1861-1864 whilst Hannah's parents were another James Kaye and wife Harriet Ninnim, nee Butler who never left England.
Annette