She would be technically eligible for transfer under the Interstate Compact for Adult Offender Supervision. She will need to apply through her probation officer (or a supervisor if they are not helpful). I see no reason why Florida would not accept her, however you should remember that the receiving state has the right to decline the application. The sentencing court can also stop the transfer at the Georgia probation officer's request.
The best thing to do here is have her attorney contact the probation officer and speak plainly about her medical condition and need to be with her family. This really shouldn't be a big deal if there are no hidden agendas. These transfers happen all the time for less compelling reasons.
Here is a link to Florida's ICAOS information. I think you will find it helpful.
Georgia's website has less information but does include that a $25 application fee is assessed for transfers.
Please reply if I can help further.
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