From researching your question a bit on the web, I would guess that the house your mother refered to was Maxwelton House (home of Annie Laurie of the famous song). The 'castle house' is located in Moniaive, which is 15 miles north west of Dumfries. I found quite a few accounts of Glasgow children being evacuated to the Moniaive
and also nearby Auldgirth
Maxwelton House is known locally as 'the house with 365 windows'. However, it is unlikely that your mother stayed there as it was allocated to the Norwegian army in exile during the war, who used the site for training a special unit of soldiers. It may be that your mother lived nearby?
There is another possibility, especially if your mother was unaccompanied by her parents, that your mother was evacuated to Cally House, a wartime residential evacuation school established by the Glasgow Education Authority in Gatehouse-of-Fleet, 30 miles south west of Dumfries.
There's a great film of Cally House on the Scottish Screen