So, you're also accessing the application through your own network and they're accessing it through the Internet.
Have you tried accessing it from a computer that's not on the network? What browser are you using? Is it different from their browser?
If everyone is using IE, there are a couple of settings that may make a difference:
1. Add your site to the trusted sites.
2. Under the Privacy tab, add your domain (mysite.com without the "www.") to the allowed sites.
-Dell
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