Do you have your fathers birth certificate. Was the sister older or yonger than her brother. Your father's mother's name should be listed. Can you look for births registered to that lady? Sandra
I'm not sure how this would help, surely if the half sister was born to another woman, she wouldn't be registered under the same name as Sharon's grandmother?
As I see it the biggest problem is that, at that time, having a child outside of a marriage was frowned upon and the facts are likely to have been kept secret. It does sound as if somethings were known, so perhaps your grandfather took some responsibility and paid towards Margaret's upbringing. As her mother moved away from the area it is also possible that she married and that Margaret was brought up thinking that man was her father.
This could be quite a delicate situation after all these years and if you do find her you need to think very carefully before contacting her as she may know nothing about another family.