Is that like "Black Jack Davy", done by Steeleye Span? Lady leaves the squire for some hoodlum heath-rover, which make for a nice song but is something I suspect few ladies of the time did.

What does Cotton Eyed Joe have to do with Women's songs? The version I know is somewhat like the one posted, but politically incorrect these days so I won't post it. You may find it on Tommy Jarrell's LP from the 1970's "Sail Away Ladies", and I don't know if it has been released on CD.