The reason for this is simply DHCP (Dynamic Host Configuration Protocol), it is a method for automatically assigning IP/Netmask, Gateway, DNS and a variety of other settings - when you have not manually configured settings.
When you manually place IP settings, it basically uses them instead of querying DHCP servers.
When you plugged in your 3G modem, it would have set up its own device independently of other network connections as you can manually set a different address on each connection. It will itself most likely be using DHCP to your ISP's server or the installer would have manually set them.
When you got home, obviously, you were connecting via the same connection as the site and their settings were taking preference over DHCP.
The way around this is to put the site settings as the "alternate configuration" and leave the main settings as DHCP, this will mean that you will always use DHCP but if it cannot find a DHCP server, it will use the settings present in the alternate configuration.