You will always have to claim your bag so you should be fine. Like you, I'm pretty hesitant about trusting my bag to make it to my "next" destination. Good part about Atlanta is that there is the Delta counter right there at "baggage recheck" so you should be in great shape.

I notice you talked about taking a shuttle to domestic. Just be aware that the airport does have a train that goes all the way through the airport -- in other words, to all the terminals. So, regardless of what terminal you arrive at, you can recheck your bag after customs, and get on the train to get to your next terminal. You do not have to get out of the terminal and take a domestic shuttle. You may have heard about the need to exit the terminal from people who are staying in Atlanta and who therefore have to exit out of Terminal F -- the new international terminal. That does not apply to those who are connecting.

You'll have lots of time--3 hours is lots of time. Also, if you happen to land in Terminal F, there are oodles of Delta people to help you there.