Provided the family can prove the dog's task training, Miami Dade will lose this one. In the official comments on the most recent ADA regulation update, DOJ already addressed the breed ban issue:http://www.ada.gov/regs2010/titleII_2010/titleII_2010_regulations.htm#a35136
"Breed limitations. A few commenters suggested that certain breeds of dogs should not be allowed to be used as service animals. Some suggested that the Department should defer to local laws restricting the breeds of dogs that individuals who reside in a community may own. Other commenters opposed breed restrictions, stating that the breed of a dog does not determine its propensity for aggression and that aggressive and non-aggressive dogs exist in all breeds.
The Department does not believe that it is either appropriate or consistent with the ADA to defer to local laws that prohibit certain breeds of dogs based on local concerns that these breeds may have a history of unprovoked aggression or attacks. Such deference would have the effect of limiting the rights of persons with disabilities under the ADA who use certain service animals based on where they live rather than on whether the use of a particular animal poses a direct threat to the health and safety of others.
Breed restrictions differ significantly from jurisdiction to jurisdiction. Some jurisdictions have no breed restrictions. Others have restrictions that, while well-meaning, have the unintended effect of screening out the very breeds of dogs that have successfully served as service animals for decades without a history of the type of unprovoked aggression or attacks that would pose a direct threat, e.g., German Shepherds. Other jurisdictions prohibit animals over a certain weight, thereby restricting breeds without invoking an express breed ban. In addition, deference to breed restrictions contained in local laws would have the unacceptable consequence of restricting travel by an individual with a disability who uses a breed that is acceptable and poses no safety hazards in the individualís home jurisdiction but is nonetheless banned by other jurisdictions.
State and local government entities have the ability to determine, on a case-by-case basis, whether a particular service animal can be excluded based on that particular animalís actual behavior or historyónot based on fears or generalizations about how an animal or breed might behave. This ability to exclude an animal whose behavior or history evidences a direct threat is sufficient to protect health and safety."
Denver and other cities have already modified city ordinances after the DOJ guidance. I'm surprised Miami Dade hasn't done the same yet, but it looks like they're still using the 1989 ordinance.http://www.miamidade.gov/animals/pitbull-law.asp