This is do-able, but I don't have enough information to advise you. Do you have a router of some type? The router is what actually gets the IP address. To be able to have a backup network, your router has to be complex enough to have multiple interfaces ( a real router - like a Cisco that has multiple interfaces).
An alternative would be to use a Windows Server with multiple network cards and setup Routing and Remote Access. Do a search on "demand dial routing" to see what come up...