There's Always an Alternative
Welcome aboard the RoadTrip America Forums!
The beauty of a RoadTrip, besides the beauty of the drive, is that you are free to drive the roads you want rather than what some mindless mapping routine tells you is the 'best' route. And often such alternative routes can easily avoid major cities and can be made for only a small price in miles driven. Such is the case for your proposed drive. Using Bloomington as a starting point, it is right around 1,125 miles to Tampa. But is there another route that would avoid Atlanta?
Well of course there is. If you can get to I-57 south fairly easily, take it to just south of Marion IL and then switch over to I-24 east to Nashville and I-65 south. Follow I-65 to Montgomery AL. There, oddly enough you will want to get on I-85 north (!) to Atlanta (!!!), but don't worry. In Montgomery, I-85 runs east-west and you're only going to use it as a connector to US-231 south which is near-freeway quality through town. South of town it becomes a four-lane divided highway, duplexed with US-82 east. While there are a few shortcuts you could take, the easiest route to follow would be to continue south on US-231 to south of Cottondale FL and get on I-10 east, then I-75 south to Tampa. That route is all of 60 miles longer than using I-75 through Atlanta and stays flatter than I-75 through the southern Appalachians.
Now, most mapping routines will tell you that an 1,000 to 1,200 mile trip can be made in 2 days, as a current retiree who used to routinely do such things, I now applaud your decision to take 2½ to 3 days. It's just more relaxing and gives you time to make a few stops along the way should there be things you'd like to see. This is especially true with a young passenger who should get some fresh air and exercise a few times each day. Also with Franklin and Dothan as your intended overnight stops, it looks like you're already planning on the route outlined above.
Now, while I usually try to take different routes to and from a destination, and Atlanta should have at least be semi-reasonable on a Saturday early evening, if you really enjoyed the trip down you can do it again on the way home. Or you can take I-75 etc. through Atlanta, Your call. Indeed if you're allowing 3 days for the drive back you could follow yet another route. One of the things I love about driving in the southeast is that even before the Interstates, many of the US highways in the area were upgraded to four-lane divided highways such as you'll experience on US-231. If you'd be interested in such roads and want to avoid all major cities, we could probably find something that would work for you.
AZBuck