If homeschooling is legal, which it is in all 50 states and many countries, then unschooling is legal.
Unschooling is simply a METHOD of homeschooling; it is not a separate thing from homeschooling. You can follow the Charlotte Mason method of homeschooling or use the Unit Studies method or you can unschool or any other approach of homeschooling that you might be comfortable with. You are still homeschooling.
In some states (and countries) unschooling can be more difficult to practice due to regulations and restrictions on homeschoolers. You might have to jump through a few more hoops (i.e., standardized testing, yearly reports, etc.) than you would if you lived elsewhere or be a bit more creative in your record-keeping.
In Alabama, church schools have their own requirements for their students (homeschoolers) and so the key is to find a church school that will work with you, that understands unschooling and welcomes unschoolers. They are out there, you just have to ask questions and be clear to the administrator as to what you are looking for. A good place to begin looking for Alabama unschooling-friendly church schools the LeapingFromTheBox.com Alabama Church School Directory.