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 :
You need to :
Go in Edit mode, some normals are flipped, recalculate them
Add some edge loops so that your armature is able to bend the object:
Reparent With Automatic Weight
Bring some corrections in Weight Paint mode
Here are the principles of bone control over vertex groups:
Let's say that I have a bone called Bone1 and a vertex group called Bone1 as well. The bone will control the vertex group that has its name (if it has been parented with an Armature Deform option). Here I assign a vertex group weight of 1 to the 2 vertices on the left, and a weight of 0.1 to the 2 ...