@BlackCapApps IK only works for one or two bones.
For your use case I would use IK for the upper and lower arm, not the hand/gun. Alternatively you would have to chain two IK chains. One with two bones and another with one bone, then make the arm constraint a child of the gun constraint. At runtime you could then do something "fancy" like having the arm constraint lag benhind the gun constraint a bit.

I'm interested in this as well. How do you pick up vertex positions from previous keys or set them precisely?

@BlackCapApps. That's a really nice animation you have going there.