How does the traffic pattern at a large airport affect nearby, smaller airports?
Generally speaking when airports like this are close together the airspace is designed to allow operations at both airports to occur without interfering with each other. 

Broadly speaking if one airport changes approach direction it may be the result of a wind change. Assuming the local prevailing winds shifted its likely the other airport will change approach direction as well due to the wind shift. 

The VFR sectional actually sheds some light on your specific area in question 


(source)

In other words, if your flying VFR its likely that IFR aircraft from the outer airfields will initial be assigned to 3000 ft. (so keep your eyes on the lookout) and if we look at the Class B floors around that area 3000 keeps you under them in most places. In a round about way you can infer that controllers are going to assign and vector you under the class B to keep you out of the ATL area. Runway turnarounds or not.