Containers don't actually affect any object's position. They simply affect the way they are picked by conditions in events. If any object is picked by an event, the rest of the objects in its container are also picked. This still makes them really useful for stuff like this though.
If we call your collider box the collider object and the look-pretty sprite the enemy, you can place the collider and enemy in a container with each other. (all you need to do is select one and add the other to its container in properties, they are both now contained)
Make sure you have an equal number of instances of collider and enemy. The event 'Always - set enemy to position of collider' will naturally match up each enemy to its contained collider.
Now you can go off making your events... anything like 'Collider collides with solid - set Enemy animation to Stopped' will affect only the associated Enemy, not all enemies like you'd expect normally. That's the magic of containers