Children keep up with their parents. Assuming your spawner isn't far off from your player, obj.global_position = global_position places the object at the exact location of the spawner. Ideally the spawner is in the position you'd want the object you want spawned, so assigning the spawned object's global position to the spawner's global position should be good enough.
However if you want your parent's position specifically:
obj.global_position = get_parent().global_position