I'm still researching this part of my family but am becoming more and more convinced that your Barneses and mine are connected.
My 3xgreat-grandparents were Samuel Barnes and Margaret Sloan.(Samuel's father was John Barnes, mother Elizabeth Candlish.) Their youngest son, Matthew, was born in 1862 in Kilmarnock, Scotland, and on his birth certificate next to that of Margaret Sloan, appeared that of Agnes Gemmell. This lady was the wife of your Robert Barnes, and the grandmother of Agnes Thomson Barnes. There are other Barnes/Gemmell connections in my family tree.
I have e-mailed you with further info.