Assuming your modem set up is for pppoe, First check your port 80 status for this you have to open/forward port in modem and router too if you want the http traffic go through it.
similarly this will apply for other ports too ..like 25,110,21,22,23 port forwarding in modem (192.168.1.x) as well as the router(192.168.2.x) as per your requirement.
start wit port 80 ..check your modem for dynamic dns setting ( you dont have to install any updater software in your machine.) and this will give access to all the connected pc in your local network (192.168.1.x and 192.168.2.x)
now open any proxy site and try to access your domain name.because from inside this will not work if your modem is in pppoe mode.
If your modem is configured for bridge mode you dont have to port forward/open in modem only router need to be configured for forwarding/open.