Go to Scotlands People website, register then sign. Select Statutory Records, then Births and complete. You should be able to locate your mothers Birth Extract which should contain the names of her parents.
If you have any problems which you cannot resolve, please let me know.

Hi,

My name is Sharleen, I'm currently researching my family tree and I'm having trouble doing my mums side. This is purely because I have no idea what her father's name was. Growing up I believed it was someone who then turned out to be impossible as I found information that he died many years before my mum was born. Having spoken to a family member, I've been advised that it's likely to be my uncles father. All we know is his father's surname was Mcginn. I believe he was in a wheelchair and had something to do with a clothes shop that my family member remembers being in St Margarets Road, Ardrossan. If anyone has any information that could help, I'd greatly appreciate it.