Show children in sidebar nav selectively

I want to show children in my sidebar nav either when on the parent page or any of the child pages.

In other words, for example, I have a section called bios (it’s a page) that has three children pages, three lawyer’s bios. I only want to show the links to the lawyers individual bios (the children of “bios”) in the sidebar nav when either on the bios page or on any of the individual bios pages. When I’m in the Articles section (a category) or in any of Article’s sub-categories, I don’t want to see any of the “bios” children anymore but I want to see the Article sub-categories listed in the sidebar nav.

How can I do this? As you can see I need to figure this out for both pages and categories.