Was there a broadside print of Child 11, The Cruel Brother during the sixteenth century?
Accordign to the notes in the John Calre book it should exist.

Looking at the Roud Index I found these entries:

Fine Flowers of the Valley
Source
Lane: Catalogue..Chapbooks & Broadsides..Harvard College No.839
Format
Printed : Street literature : Broadside / Chapbook catalogue
Src Contents
Reference only

It's just a reference, there's no text to go by.

And another one:

The Cruel Brother

First Line
There was three ladies play'd at the ba'
Source
Tragical Ballad of Lord John's Murder, The
Format
Printed : Street literature : Chapbook
Printer / Publisher
[For the Booksellers] (Glasgow) No.79


Here's the text for that one:
http://digital.nls.uk/chapbooks-printed-in-scotland/archive/108701622?mode=fulls

Together with The cruel brother. Glasgow : Printed for the booksellers, [1840-1850?].

But the date is too late.
I can't find anything earlier than that.