Hi Gillian and a warm welcome to RootsChat from me too.
I don't know if you have checked out
www.scotlandspeople.gov.uk website where all the original records of birth/marriages/deaths are available online. It is very easy to register and you buy credits to download and view. Check it out for yourself.
My condolences on the loss of your dad.
Following on from Sandra's post about the tree on anc I looked at the dates given and then went on to check the Index on Scotlands People to verify the information.
What I found was the following -
There is a marriage in 1912 between Robert Drummond Duncan and Janet Bowie Gray Thomson. Deaths for Robert and Janet in 1961 ages given as 72 and 68.
Then to the 2 girls from the anc tree - Annie Thomson Drummond Duncan was born in 1927 and her older sister - Janet Drummond Duncan in 1920.
Now this brings me back to your dad's birth certificate. From his mother's age at death this would mean she was born around 1893 and gave birth to your dad aged 45. Not impossible but why did she say her husband Robert was deceased?? when he did not die until 1961.
Two possibilities here either they were divorced or separated and she was unsure if he was still alive but gave his name anyway. The other possibility which is a bit sensitive is that he was actually the son of their daughter Janet Drummond Duncan born in 1920.
I have a similar situation in my family where the granny registered a birth as hers to save the stigma of illegitimacy.
Do you have any further family information e.g. Aunts/Uncles of your dad?
Please let us know if we can help you further.
Dorrie
P.S. Just an update on the two girls.
Annie appears to have gone to America and died there in 2003 - unconfirmed but there are two records for her arriving back in the UK in the 1950's and the address she is going to is 51 Castleview Terrace, Haggs, Stirlingshire.
Janet married a William Carson in Glasgow in 1939 and died in Glenrothes, Fife in 2008. According to the tree on anc there are 4 living children.