Parent / child is badly named in the UI because they aren't really parent-child relationships, they are just related streams. Streams can have multiple "parents" so if it was reflected in the URL, you'd have multiple URLs for the same stream.
I agree that the RHS should order by last updated, however...
With the branching epic we've just started working on, most of these issues will become moot (and even the way I'm responding to you now will too).