highlight parent page on menu when child page is on sidebar (and not on menu)

I do this quite often, actually, if I’m understanding your issue correctly. If you use Appearance > menus, and create your navigation (with dropdown/children), then pull in the Custom Menu widget into the sidebar, you can use CSS to handle the rest.

Basically, you just set the main navigation in the header to how the regular list items, but hide the children. Something like:

#header .menu li li {
  display:none;
}

That will show the main links in the header, but hide the dropdowns.

Because you’re pulling the same menu into the sidebar via the widget, the classes you need to highlight the menu items (for the current page you’re on) are already set – all you have to do it style them.