I think you will probably find that Euphemia's parents were David Arklay and Margaret Stewart, but that you will not find her birth or baptism record.
I have got Jane in the 1881 census. At 52 Ure Street, parish of Liff and Benvie*, were David Arklay, 52, Jute weaver, born Forfar, Angus; Margaret Arklay, 55, born Inchture, Perthshire; John Arklay, son, 21, born Dundee; Stewart Arklay, 15, grocer's shop boy, born Dundee; Jane Abbot, granddaughter, 7, born Dundee.
*Liff and Benvie is the neighbouring parish to the parish of Dundee. The city of Dundee had spread out to cover quite a lot of the parish of Liff and Benvie by 1881.
The index shows Margaret Arklay, 64, and Jane Abbot, 17, both at the same address in Dundee in 1891. In 1901 Margaret Arklay, 75, and Jane Abbot, 26, are both in Dundee, but not at the same address. Neither is there in 1911.
A David Arklay, 75, died in Lochee (another neighbouring parish largely taken into the city) in 1904 and Margaret Arklay or Stewart, 75, died in Dundee in 1901. Their death certificates should tell you the names of their parents, including mothers' maiden surnames.
Jane may have married or emigrated. There is a possible death of a Jane Abbot, or Welsh, 66, in Glasgow in 1942, but I think this is Jane Welsh, wife of Peter Abbot.