Máire Bhruinneal means "grown-up Mary".
I wonder if you're actually looking for a song called
"An Mhaighdean Mhara" - The Mermaid - which has a line
where the mermaid mother is swimming out at sea and
singing in to her children, Máire and Pádraig, and
she refers to "Máire bhruinneal".
If so, you'll find the words on an album called
Amhráin ar an Sean-Nós, published by RTE in Ireland.
It's available through Claddagh Records in Cecilia