It's not covers all cases, but you can use Shrink/Flatten (Alt+S) instead of regular Scale. It uses normals for transformation, so for circles it should work fine.
The Problem, that you have is about center of objects. When you use mirror, transform tool use center of vertexes, instead center of symmetry. So for make it work as you expect, you should use 3D-cursor to define center of transformation. See here: