Personally I would just connect the 3G when I need to browse the web, just accept it will disconnect things and then disconnect the 3G when I have finished.
If you do want to get around it you could add routes similar to the following on your PC at a command prompt -
route add Y.Y.Y.Y mask Z.Z.Z.Z X.X.X.X
where Y.Y.Y.Y is any subnet you wish to reach on your work LAN
where Z.Z.Z.Z is the subnet mask for the above subnet
where X.X.X.X is your work LAN default gateway address
This should allow you to access what you need to at work but still allow you to browse the web via the 3G dongle. These route statements are removed when you reboot so if they cause any problems just reboot and they will be gone. If it works and you want to keep them then add a '-p' to the end of the line when you enter the route and it will then be persistent across reboots.
If you want a bit more info about the command just type 'route' in a command prompt, hit enter and it will give you the help notes.
Hope that all makes sense and that I've got the right end of the stick. Seems like it should work in my head but give it a go if you like and see
Paul.