Sounds to me like your laptop settings are at fault. You need to change these when you use different hotspots.
You can get network profile software that will store and change these for you automatically but you need to get your TCP / IP settings correct first as it sounds like your laptop is set specifically to use your iphone at the moment.
As for the iphone, it's providing a basic wifi access point. I would be surprised if its capable of acting as a bridge to another network but its not impossible. You'd probably need to find an app for it though.