Had another look - in 1881 she was born "Eversdon" and was a teacher of music and French at Crispigney House in Suffolk, and in 1871 and 1861 with her parents at Modbury. 1861 shows that she was actually not the eldest - there's a son, George R, aged 4, with them in 1861.
And I located her in 1901! Age is listed as 48, probably meant to be 43 and transcribed wrongly - she was living in New Windsor, Berkshire, and is indeed listed as 'author'!.
Also her death was reported in the Times:
The Times, Friday, Aug 29, 1924; pg. 1; Issue 43743; col A
On the 23rd Aug, Emma Martha Green, eldest daughter of the late Revd. G. C. Green, Vicar of Modbury, aged 66.
From the death index images:
Emma M. Green, aged 66, Kingsbridge district, volume 5b page 211 (September quarter 1924 deaths). Kingsbridge district is in Devon and includes Modbury.
http://genuki.cs.ncl.ac.uk/DEV/Modbury/ModburyKelly1923.html - 1923 directory for Modbury shows the "Misses Green" living on Church Street - could be Emma and sisters?
http://genuki.cs.ncl.ac.uk/DEV/Modbury/ModburyKelly1930.html - 1930 gives address as "17 Church Street"
http://genuki.cs.ncl.ac.uk/DEV/Modbury/ModburyKelly1935.html - by 1935 it is 'Miss' Green, singular.
http://www.modbury-heritage.co.uk/index.htm - Modbury seems to have an active local history/heritage group who might be able to help. They seem to have some information related to her father, at least.
ETA: the 1930 and 1935 directories make reference to a memorial to "Miss Emma Green", daughter of the late vicar!