.fbx export animation is incorrect

Hello folks.

I uploaded a video of my problem:

I have a problem exporting to an .fbx file in Blender.
I want to create a reload animation. In the scene there is a body with bones and the weapon with bones. The bones of the weapon are connected to the middle bones of the hand via a constraint (child of), so that the weapon follows the movement of the hand.

When I export the whole thing as .fbx to insert the animation into unity, the hand wobbles around the weapon during the animation. This looks extremely bad in the game. how could I solve this?

Many thanks in advance.
Best regards.