What I'm looking for seems like basic website navigation, so I'm surprised it's not in core WordPress. I want to have a "section menu" or "context menu" (I'm not sure of the right term) that will change depending on what page in the hierarchy is being viewed, showing only related items. I'm happy to create custom menus for the task, but I don't know how to control when they are visible and when they aren't.
The plugin "Subpages in Context" comes close, but it shows the menu even when the viewed page has no children (e.g. an About page or Contact Us), which looks silly. Also, it would be nice to have the ability to shorten titles for some of the menu items - some of my page titles are longer than I would like on the menu, ideally.
I also tried the "Section Widget" plugin (the simple part - I don't need the tabs). It has good control of when the content would be shown (just select the page checkboxes), but I would have to write the HTML for the menus by hand - that's pretty tedious, prone to errors, and not helpful for handing the maintenance of the site over to a non-programmer.
The Custom Menu functionality in core WordPress works well for creating the menus, if I could find a way to conditionally show them, like placing them inside the "Section Widget" or something, but that doesn't look possible.
Isn't this something that lots of people would want to do? Ideas are appreciated.