There is a death showing in Edinburgh in 1873 for a Jemima Brown Aitchison which would fit with the Kate's mother showing as deceased at the time of the 1886 marriage.
This is the closest I can see in the 1881 census with a possible second marriage for father Thomas - everyone showing as born in Edinburgh unless shown:
Thomas S Aitchison 50, Surgeon Dentist
Anna Aitchison 28, wife, b. England
James Aitchison 26, son, dentist
Thomas S Aitchison 22, son, Ranoforte (pianoforte?) Tuner
Jemima B Aitchison 20, daughter
David W Aitchison 16, son, dentist
Catherine Aitchison 14, daughter
Emily L Aitchison 10, daughter
Mary Davie 17, servant b. Linlithgow
Address: 61 Queen Street, Edinburgh
Monica