Sorry to bother your guys again, and thanks gnu for all the help you have given me so far.
I am looking into other theories, even though they maybe remote. I can see from the 1861 census that the Plunkett family had a lodger called "Ellen Rooney". Now I know that Susanna married Patrick Rooney after her first husband Alexander Plunkett died in 1863. I wonder if this Ellen is somehow related to Patrick. Anyway Ellen is also the middle name of Mary Ellen who was born in 1861. Could it be that Ellen was the real mother of Mary Ellen and something happened to Ellen and Susanna and family adopted her?. Would Mary Ellen's birth cert show this? I may order it. The only thing against this theory is that Mary Ellen has always put Alexander as her father in all her certs, even if she sometimes put Mary instead of Susanna as her mother. Alexander died in 1863 when Mary Ellen was two years old so she would not remember him. Therefore I doubt she would list her as her father unless she was sure he was her real father. It would make more sense to list Rooney as her father, a man who she grew up with.
Also Agnes was with her grandmother Susan in the 1891 census. I can see Mary Ellen had a large family when she was in Bothwell in 1891. Could it be that her mother had not enough room in her house to keep her so sent her to live with grandparents? Is that the most likely explanation.
Thanks again
Robert