If you have a parent layer in After Effects with animation applied and a child object that follows the parents position, and you want to create a wiggle expression fro the child layer, You may find that the child will wiggle according to the expression however, it no longer moves with the parent and stays put.
The key is behind the PickWhip in After Effects where PickWhipping an attribute to another attribute such as position will behave like a parent; However it is not a parent in its truest form.
Here, Jonathan Berkey shows us how you are able to add a wiggle expression in After EFfects to the parented layer and have the parent behavior to remain intact. One of the methods to do this is to add the wiggle expression to the anchor point of the child layer rather than the position attribute.
The next method may seem like a straight forward and simple concept if you are coming from or are accustom to creating animations in 3D applications, and it may seem like the only clear method to you.
If you were to parent the two layers together and NOT PickWhip their position values, then everything will behave as expected. This is a huge distinction in the functionality of parenting in After Effects and simply PickWhipping like attributes. This will leave the position attribute in the child layer free for a wiggle expression.