Kate Seaby (Badcock?): appears twice on 1911 census

Kate Seaby is my first cousin twice-removed (or would be if she is still alive). She was born in 1900, a year before all four of my grandparents were born. Her mother was Margaret Jane Seaby, sister to my great-grandmother Lavinia Brown (nee Seaby). Her father is unknown but may have been Margaret's 'husband' and uncle, William Badcock, the brother of Margaret's mother Emma Seaby (nee Badcock). The questions around Margaret and William's marriage and children have been recorded here before. The 1911 census is the first where I have found an ancestor appearing twice, although I understand that this is not unheard of.

I first found Kate in 1911, aged 11, living with her mother Margaret Jane and Margaret's husband Albert Stonebridge at Edinburgh Farm, Dry Drayton. Albert was aged 44 and described as 'agricultural labourer on farm'; Margaret, his wife of seven years, is 41. Children described as Albert's sons and daughters are: Ernest Seaby (17), agricultural labourer on farm; Kate Seaby, 11, at school; Adelaide Stonebridge, 6 and Bessie Stonebridge, 4, both also at school. Margaret says she has had 7 children in all, with six still living.

But when I searched for Margaret's mother, who married Jonathan Trevis in 1891 after her first husband, William Seaby, died, I found Kate again, this time in her grandmother's household. Emma Trevis is a 78 year old widow who made her mark in the 'signature' field on the census. She says she has had ten children in all, with four still living.