Full-Width Sub-Nav in Twenty Thirteen Child Theme

I have a navigation system with some parent pages and child pages. When you hover over the parent pages, I would like the sub-menus to display horizontally just beneath the main nav. I’ve almost got it working, but I’m stuck on one thing. I want the sub-nav background to extend the full-width of the frame (and it needs to be responsive so that it extends the full-width no matter the browser size). Is there any way to do this?

Here’s the site I’m working on so you can see what I’m talking about.

Thanks.