Why isn’t my slider filling up the screens width?

The slider can be only as wide, as the container. This width is depending on the template

For Joomla, the best solution is to make an other module position, which doesn’t have any containers with maximum width styles. You can find a documentation here, how you can find a code part in your template. Here is a tutorial, how to make a module position, which works on Joomla 2.5 and 3 too. 

For WordPress, the best solution is putting the PHP code into a php file, where the container isn't limited. You can find the documentation on how to do that here.