Sounds like you're almost there! And yes, deleting the mobile subdomain is a good idea only once you've successfully STOPPED sending people to it :) Better to have people land on a bogus page than a dead domain.
Are you working with anyone else, or is it just you? What's interesting is that it seems like SOMEONE intentionally set this up. GoDaddy can give you all the free subdomains it wants, but nothing is going to "accidentally" implement a javascript include in your WordPress code for you - unless... did you install WP as an "app" from GoDaddy? Knowing that you're hosted with them, it's possible they're doing something weird/magic on you.
The JS include is likely going to be inside one of your theme files, not a core WP file. Check /wp-content/themes/YOURTHEME/header.php - that would be my best guess on where you'll probably find it.
If you really struggle to find it, download a full copy of your whole WordPress install (if you don't already have one) and use a program like Notepad++ that allows you to "Find in Files". You can target the entire directory, plug in your search string ("dudamobile.com") and you should be able to find it then.
Good luck!