If you are using a plugin for the popup, and it's not doing what you want, then you need to ask the plugin author for support.
From the screenshot, it looks like you're using an iframe, which means you're basically just loading the whole site a second time. If that's what you're doing, you may have more success using this plugin to pull just the post content instead: https://wordpress.org/plugins/improved-include-page/
Without being able to actually see the site and inspect it with Firebug
, I can't make any suggestions as to how to do it better.