Hi Mikey,
We've got lots of great whitewater here in AL when its rainy season. We usually have plenty of water Dec - March. Sometimes the water dries up in April, sometimes things run into June. You never really can tell. You will have to endure August in AL which is miserable but at least you would no longer have to deal with the brutal winters of MI - you'll be paddling while everyone up north is shoveling snow
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Most of the whitewater in AL is east of I-65 and north of I-85 - with a huge variety of class 2-5 rivers ranging from big water to steep creeking. There are also some very interesting small canyon runs north of I-22 and west of I-65 - though more in the class 1-2 range. AL is a surprisingly varied and beautiful state.
When the water dries up in the summer, the ocoee is about 3 hrs away from birmingham and there are several dam controlled piedmont rivers along I-85 - the best of which is the chattahoochee in columbus.
The alabamawhitewater website that Wendy posted above is the definitive resource. If you check Kirk Eddlemon's newest books you'll see he has info on the Little River Canyon area, the creeks of Sand Mountain, and staples like the Mulberry and Locust Fork of the Warrior among others.
There are also very active paddling clubs in Birmingham and Huntsville.
Not sure about job opportunities in B'ham - depends on your wife and son's field I guess. Birmingham does have a lot of jobs in the health care industry with UAB, St Vincents, Andrews Clinic etc in town.
Anyway hope that helps.
to be expected I suppose, although I do see it's the 3rd rainiest city in the US 
