Interstate Extradition is limited to offenses that constitute a crime. Even assuming that IA treats DUI/DWI offenses as a criminal offense (as well as a MV offense), it is probably not likely that IA would extradite him from FLA, as extradition is generally only used when there is a significant criminal interest on the part of the requesting State (IA).
On the other hand, the IA warrant can be used to suspend his license in FLA until he returns to IA to deal with the DUI. Whether the Public Defender knew of his out-of-State staus or not, would not stop the Court from issuing a warrant for failure to appear. I suggest that he check his license status on a regular basis to make sure he is not suspended in FLA; that he check with the FLA Motor Vehicle agency to determine what they will do to his license privileges in FLA if he is convicted of the DUI in IA; that he contact the IA lawyer who was handling the DUI to see what his alternatives are in regards to beating the DUI; and, that he contact the Court in IA to see what it will take to get the warrant in IA lifted. Good luck.
This answer does not create an attorney-client relationship or constitute legal advice. Given the nature of this website, it is provided solely for informational purposes, for you to use as a starting point when speaking directly with a lawyer in your State. Do not assume that the legal theories I mention that pertain to NJ will apply in your State. I urge you to immediately contact an experienced criminal defense lawyer admitted to practice in your State before making any decisions about this case.
Your question is somewhat muddled.
The simple answer is that it would be up to the Iowa Governor's office. My gut feeling is they would not extradite for a misdemeanor offense, but at the same time, you could see your husband continually being re-arrested on the Iowa warrant and detained for several days until the Iowa Governor's office formally declines to extradite to Iowa.
I would suggest just serving the one day and getting the case over with. Plus, he will never be able to get a driver license in Florida until he clears up the Iowa case.
An extradition occurs only if the crime is a felony offense. In Florida only the third DUI is a felony. Iowa has no need to extradite because they are members of the Interstate Compact Among Member states which most states agree to uphold and allows suspensions in other states to find you and reach out to you . A suspension is on the way. At this point it is just a matter of time.
I am surprised Iowa allowed you to utilize the services of the Public Defender as most states require you to be in the state when they are appointed. My former partner is the Chief Public Defender and I can tell you there are many functions an attorney performs that the Office of the Public Defender is not allowed to be involved in, i.g. lifting the suspension on your driver's license.
In Florida you can go to the Clerk of the court, traffic Division and they will provide you with a lifetime driving record for three dollars per page...do this every three months. Most importantly, you need to change your address with the clerks office in Iowa if you want to be in the loop. Additionally, if the Judge sees that you are trying to keep them informed, they may wait to suspend you because you are being responsible...but don't hold your breath. It is never a good idea to let any traffic charge go to default.