Hi!
I took a look at the rig, the problem is that the group that you are scaling has both the joints as well as the geometry in that is skinned to them in it. This causes double transformation of the skinned meshes. The wings are not skinned, thats why they don't follow and the joints are actually the only thing that scales correctly.
Your "Null" group also has some kind of transforms on them which cause problems when working with the Hierarchy of the skinned meshes because their Transforms are locked due to skinning.
But its acutally a rather easy fix.
1) Duplicate the "Null" Group and delete everything in the duplicate, you just need a group that has the same transforms as "Null" because of the problem mentioned above.
2) Parent all the skinned mesh Nodes (the Mesh node in Null that don't have any other groups above them) into the duplicate.
3) Parent the "dome" group under "Null"
Your Hierarchy in the End should look like this:

This should allow you to scale the "Null" group and get the scaling you want. Normally you would want every Mesh that is Animated in a rig to be skinned (so the wings and dome as well) but it shouldn't cause too many problems in this case.
I hope this helps!