Thanks you all for your replies!
I do actually have all of that information through ScotlandsPeople. I have copies of Annie's marriage to both John and James, I have Annie's birth certificate etc. I also have her son Thomas's death certificate. (I ordered it because I wanted to help find my Grandfather's brother for him; and sadly had to tell him his brother passed away in 1986, as I also had to tell him his elder half brother John passed away in 2014). I have as yet been unable to track down his younger half sister 'Betty', but remember my Grandfather telling me when their mother passed away from TB when he was 10, they went to live with his Grandmother (Annie's mother) in Plantation. 'Betty' was 1 year old at the most. He told me when he went to National Service, he used to send the bulk of his wage back to his Grandmother to help with raising Thomas and Betty.
I am unsure how to track down whatever happened to Betty after Jane McElroy, their Grandmother raising them, passed away. Betty would have been approx. 16.
I have ordered James Mitchell's Death Certificate also.
I guess I was more hoping that maybe someone might have known someone who knew Annie and James, and consequently their infant daughter 'Betty'.
Unfortunately my Grandfather has just passed away so I'll never be able to tell him what happened to his sister, but I'd love to know
Thank you all