How to synchronize layer position variation in After Effects?

In addition to Rick's excellent suggestions, if you want circle shape layer 2 to keep its own keyframed/expression motion but also inherit the motion of circle shape layer 1, you could use a position expression like this:

p = thisComp.layer("circle shape layer 1").transform.position;
value + p - p.valueAtTime(0)

Wiggle layer 1, then make Layer 2 the child of layer 1. Use the dropdown menu or the pickwhip in the Parent/Link column of the timeline. (Shift + F4 shows and hides the column)

Or, put both circles on the same shape layer.