Question: What is the history behind the dancing of the Mazinka. Does the wreath that is worn have to be made up of specific greenery or flowers?
Answer: The name of the Mezinka dance comes from a song composed by Morris Warshavsky (1848-1907). You can find the full lyrics here.
The word Mezinka means "youngest daughter."
I have not found a definitive source for the tradition, but since the song was likely written in the late 19th century, I would guess that the custom dates from the same time period (since one could not dance the mezinke before the song was written!). It is possible, however, that there was a folk tradition to dance around the mother at the marriage of her youngest daughter even before this song was written.
The wreath, which is a variation on/addition to the dance itself, is made of flowers - I found no more specific references than this.