Hello, will attempt to pay it forward as others have done for me on these forums. I am building a rather complex site using the Responsive theme as my base, so I am fairly familiar. Anyway, I would recommend the following:
1. make sure you are using a child theme
2. make a custom page template using your Home page
3. then simply add another div below your widgets and above the footer
4. whatever you name your new div (class), you will need to add/edit the CSS for it to make sure that it expands full width
Also, make sure that your new div is not 'inside' the main content div as these have their widths set by the CSS styling from lines 261 to 307.
I really hope this helps. I rarely am ever here so good luck, if you need help with numbers 1 or 2 simply youtube it or head to the WP codex which is actually very well written and easy to understand.