BHM is what...4 hours away?
That to me means some gas money and 4 good CDs. Comparing a commute you can DRIVE to in a pinch and a guy who lives on the other side of the Rockies is night and day. You can make BHM work--easy.
I always advise guys that IF they are happy where they are, then STAY there for 12 months. You have so many new things to learn--let the wife and kids keep the same schools, chuch, and social circles while you get your hands around this new life. You have NO idea what trips/flying you'll like...yet. Fly the line a while, then assess what you think works for you. If you are bailing from the military, you likely are taking a "temporary" pay cut. Why try to buy a new house, deal with all the associated moving expenses, etc in an already stressful situation? Your second year, you can use your vacation time, bid a month off, and move at YOUR convenience. You'll have a better W-2 and you won't be on probation--not a big deal but might make signing that big mortgage a bit less stressful.
You may decide to move to MEM...lots of folks do and are quite happy. I've also know a few who did the "auto move" and later regretted it...ended up moving again AWAY. Commuting for 4-12 months ain't THAT tough, and will allow you to carefully examine your options and see what works best for you. B'ham....geez...if you were badass you could ride a bike to work in a pinch. If you like it there, I don't think it will be that tough.
FWIW...I live where my Guard base is as well. It works great for our family. I think double-commutes make both jobs miserable, but being next to one or the other makes the combo a nice package.
Good luck--it IS worth all the effort, time, and research...