I'm new to Enyo and am trying to implement display interface for my website within an Enyo app.
Basically all that I want to display is the app's toolbar on the top of the page, and the rest of the page would simply display the contents of my website.
Considering that my website is already optimized for responsive display, how do I implement this without encountering Cross-Origin issues?
I think you'll want to embed your site's contents within an iFrame. You haven't said whether the app buttons will need to interact with your site's contents so you may run into some issues there.
You don't quite have enough detail for a better answer. What cross-origin problems do you predict? Where will you be deploying? Will you be pulling the site live or will you have a cached copy you distribute with the Enyo app?