Components don’t “move” their parents unless they are all simulating and constrained to each other, that isn’t how the engine works. Parents move their children in engine.
You are free to grip the pump as the primary slot location and visually have the handle change with an addition offset or skeletal animation and have the rear hand be the secondary, or you can run it with multiple physics grips and the gun as simulating, or you could run a custom grip and sync the gun to the grip somehow taking into account it sliding in relative space…
However, moving a sub component, never moves its parent, you’ll have to re-think how you want to implement it, game engines aren’t real life and some things don’t “just work”.