Are you still able to access your website even with the second connection?

There could be some program on your PC which is making the second connection. Or maybe there is something wrong with your router. Connect your PC directly to the Net by-passing the router to see what happens.

If the router has a built-in firewall, set it to block the second IP and see what happens. Or install a software firewall on your PC and block traffic for the second IP connection and see what happens.