Disabling a rigidbody

Wouldn't recommend disabling the rigidbody. Try this instead. It turns off gravity and forces, basically.

 gameObject.GetComponent<RigidBody>().isKinematic = true;

As for WHEN to apply the change, it seems like your code might be a bit of a mess from your description... when you grab and release it, you should be applying the settings then in that same code.

Assuming you're changing the parent somewhere in your code, you can do this:

     grabbableObject.transform.SetParent(newParent.transform);
     
     if(newParent.tag == "player")
     {
         RigidBody objectRigidBody = grabbableObject.GetComponent<RigidBody>();
     
         if(objectRigidBody  != null)
         {
             objectRigidBody.enabled = false;
         }
      }