>> I ordinarily need to use a Firefox Add-In to check the browser width and have another that emulates specific mobile devices.

Why? In the default menu (no add-ins needed, but Firebug is nice), Web Developer Options, Responsive Design View lets you choose a preset size to emulate (defaults are common device screen sizes) or scale to any size, without changing your browser window size. The responsive frameworks I've seen only care about screen size (if they aren't completely fluid). Trying to keep track of all the different devices is a nightmare that becomes even worse if you consider mobile Safari, native Android, Chrome, Firefox, Opera, Dolphin, IE (on Windows Phone), whatever Blackberry is running, etc.