Unfortunately, if you physically live in Alabama, but don't keep a permanent residence in Georgia (although you may be voting and working there), your circumstances would technically make you a legal resident (domiciled for tax purposes) in Alabama.
Since you work in Georgia, your Georgia income would be subject to Georgia taxation. Also, since you are domiciled in Alabama, the state of Alabama taxes you on all of your income, no matter where it is earned, even if just across the state border.
So, you're faced with the prospect of what is known as "double-taxed" income. How does this get resolved fairly? Well, you will want to file a nonresident Georgia state tax return, and report your Georgia-source income there. Then, when you file your Alabama resident tax return, you will claim an Alabama state tax credit for income taxes paid to Georgia.
Effectively, then, you either eliminate (or at least substantially reduce) your "mutually-taxed" income on a state level. Of course, the federal government (IRS) taxes your income the same in whatever state is is earned.
Now, then, in TurboTax, the order sequence of tax preparation is crucial. If the taxpayer does not go through the sequence correctly, then the state tax credit may not be calculation properly. That correct tax preparation order is:
1) Finish your Federal tax return first
2) Finish your nonresident (Georgia) tax return second
3) Finish your resident (Alabama) tax return third
Finally, there appears to be a source of local tax help available to you on Fort Benning itself. Here is a link to the information I researched for you:
http://www.benning.army.mil/mcoe/sja/Tax.html