I don't want to close the door yet on the possibility that my partner might be related to the famous and academic Peterson family of Scottish/Norweigan descent.
Her great-grandfather Gulam Mohamed could have had a relationship, even married, one of the daughters of John Peterson (merchant) and Grace Montford (nee Anderson). These daughters were:
- ANN PETERSON b.6 JUN 1845 in South Leith, Midlothian
- BARBARA MANN PETERSON b.29 NOV 1848 at Saint Cuthberts, Edinburgh, Midlothian
- MARGARET GRACE PETERSON b.25 NOV 1862 at Saint Cuthberts, Edinburgh, Midlothian
- GUILILMA FRANCES PETERSON b.17 MAR 1869 at Saint Cuthberts, Edinburgh, Midlothian
Date-wise, the last two seem most likely, but I can't find any more information about them.