The search: 'Hawthorne and battered and aubrey' gets 2 hits in Lexis Academic, Legal Research / State Case Law / Florida / All Courts,All dates:

470 So. 2d 770; 1985 Fla. App
408 So. 2d 801; 1982 Fla. App

It would be possible to trace backward, in the references at the end of these decisions, to see what precedents the judges used to decide the 2 appeals.

A cheaper approach, if you can't get access to Lexis, is a web search for cases or online articles that cite these cases. "470 So. 2d 770" gets 25 hits in google.com , "408 So. 2d 80" gets 2 hits, including a Florida State Law Library 114 page pdf copy of a decision that cites this case - and many others. But to get the full text of the 2 Hawthorne v State cases, you will need to get to a library that has Lexis or Westlaw or other full text case collections.

I suspect that given enough persistence and time, you might well find reference(s) to an earlier case or cases on the web - and then be able to get an interlibrary loan copy of the full text, via your nearby public or college library. But it may pay you in the long run to make the drive or train ride to a big academic library that has Lexis (check first to be sure on-site access is not restricted to students only).

Some possible links to try are

Herstory Timeline of Domestic Violence:
http://www.mincava.umn.edu/documents/herstory/herstory.html

-and-

National Clearinghouse for the Defense of Battered Women:
http://www.bwjp.org/