Subtract the weights of one vertex group from another I have an issue with a rig (this is my first time rigging) where it requires the subtraction of the weights of many different Vertex Groups from the head (root) vertex group to make the rig function properly.  

Here is an image showing what I wish to accomplish:



The result image is an inversion of the middle image. Do keep in mind that inversion will not cut it, since I have to remove more things from the head (root) vertex group other than just the jaw itself.

Using the remove button in the vertex group tab gives me this result



This is not satisfactory, as it removes the vertices from the vertex group, but does not subtract the weight values from it.

Google has not turned up anything so far.

Normalizing solves nothing as it still causes deformation when moving parts with Children i.e. opening and closing the jaw deforms the lower lip bones.

Removing the influence of the head (root) bone will also cause irregular behavior as well since Blender treats all weights which aren't zero as one regardless of the weight assigned due to the vertices needing a weight of one.
You can use a Vertex Weight Mix modifier.
Say you have Vertex Group A :

And B :

In order to subtract B from A, add a Vertex Weight Mix set to Subtract and to effect only group A.
Result when viewing the A Group after adding the modifier :