Sorry to hear you're having issues with streaming your Slingbox outside of your home network. This sounds like a port forwarding issue. There is a great web site that will walk you through step by step instructions on port forwarding your router. The web site is port forward.com and you will need the router manufacturer and model number. Since you do have a double router setup you may have to port forward both. This is also something you can contact your router manufacturer about and they may be able to do for you.
Once you open the ports on your router you should not have any issue with connecting to your Slingbox outside of your home network.
Sling Moderation Team