Other than deleting features, a configuration involving composite relationship class with backward direction will require require custom programming. Please see the note "No other effect unless custom behavior is programmed" listed in the chart about two-thirds of the way down in the Relationship Class Properties help section. You can swap your destination and origin and then change the relationship class properties to use composite with forward direction, OR you can simply modify you current configuration and change the direction flow to Both rather than Backward.
Interesting. What happens if you move/rotate a feature in the origin? Does the related feature in the destination move as a result? Also, are you using an ArcView, ArcEditor, or ArcInfo license?
That's great! So yes, depending on which feature class should be moved and which should move as a result (related) you would set up your relationship class accordingly using composite and "Both". Does this answer your question?
Based on my understanding of the chart from the link I posted earlier in this thread, and based on the results of your testing, I am just as curious as you are about these settings. For both simple and composite relationships, the chart seems clear in describing the intended behavior but for whatever reason the observed behavior is different. Perhaps other members of the forum, and/or someone from Esri, will comment on their experiences with relationship classes.