With that link above, you need to pay particular attention to the "module positions" and "basic customisation" documentation.
If your submenu names are too long, then you really need to consider making them shorter. When designing your website navigation "less is more" should be your mantra.
I can see you working on your site as we're talking too ... looks like you got your module working on the AHA page. Check the settings there and make sure your "menu assignment" includes all of the pages you want that module to appear on (something I forgot to mention earlier).