The other place that you could check is the Kirk Sessions records for the parish where her mother was living when she was born (you should have the parish from the birth certificate).
Although many have been digitised, at present these are not available online. You would have to visit one of the local archives in Scotland that have access to the collection.
There are plans to make these (and other court) records more widely available via the ScotlandsPeople website. You may already be familiar with this site if that's where you obtained the birth, marriage and death certificates.
It may be worth signing up for their email updates so that you are kept informed of the latest additions to records on the site.