Thanks for your reply. Having spent a number of years looking for the family of George Hunter; I am still quite sure that he is the son or at very least related to Jane Hunter (née Barnes).
From the Families In British India Society (FIBIS) database, there is the record of George Hunter from Massoorie (likely to be a typographical error for Mussoorie) who is the son and heir of Jane Barnes who died 22 Apr 1868 in Aberdeen. My great x3 grandfather lived in Mussoorie in 1868 and Mussoorie was much smaller than it is now. The population of Mussoorie was between 2-3 thousand as one needed a permit to be able to live in the town. As far as I am aware, my George Hunter was the only George Hunter living in Mussoorie at that time and should therefore be the person mentioned in the FIBIS record.
The FIBIS record states that Jane Hunter (née Barnes) died one day after your Jane Hunter. With just one day difference between the recorded dates, I believe the FIBIS entry maybe a transcription error. I have come across this situation before and considering some of the other evidence, I believe that this is the same person. For example the marriage certificate of George Hunter shows George's father was Robert Hunter and your Jane Barnes was married to a Robert Hunter.
It would also appear that although George started out on his own in India, he became quite successful and even tutored Maharajah Duleep Singh. The Maharajah resided at the Castle in Mussoorie, the house on top of Castle Hill. The house belonged to Mr. Henry Vansittart, the second husband of Mary Amelia Dobbie, who happens to be the ex wife of William Jervis (my great (x4) grand/great uncle). George Hunter owned the Belleville estate which, when he married Catherine Jervis, was bought by the town and became the Town Hall. George then resided at Sylverton house with his family until his death in 1886. The Sylverton house remained in the family until at least 1919.
If you would like to know more about George and his descendents then please just drop me a line.