Technically, there is no such thing as a "hardship" driver license in the state of Alabama. Either one holds a driver license or does not. While other states use the term "hardship" or "occupational/limited privilege" or "work permit" driver license to signify a type of limited privilege driver license, the state of Alabama does not issue or utilize such category of driver license.
If a person is revoked by an out of state jurisdiction and such revocation order is either permanent (lifetime) or for such long duration that exceeds Alabama's statutory limitation on revocation orders, and is a permanent resident of the state of Alabama for at least one year, then that person may apply for a "Welch Hearing" to determine suitability to obtain an Alabama driver license. See the Avvo Legal Guide under this topic - 'Welch Hearings'. Please note that even if the state of Alabama did issue a driver license under the Welch Hearing process, it would not authorize a person to legally operate in the former state where the license or privilege remained revoked or disqualified.
Normally you will not be able to deal with another state regarding your driving privileges if your home state has taken away your license, so you'll need to get valid with Florida before another state will deal with you. If you get the hardship license set up in Florida, it may cover your travel in Alabama, but you'll want to discuss that with the Florida DMV to see what options they offer. If the options don't work, you should consult with an attorney who handles DUI offenses in Florida for other ideas. You can find many experienced candidates on this website in Florida.
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