Just thinking. But....
You take two, sew (or something) them together so that the brim/bill is that the same place but only sew it about half way so that the hat part makes a bag and where the brim is becomes the opening for the purse. The brim could become the handles - you could even make a cut out in them for hands. And of course you would want a lining in it.
hope that makes sense to you.