If my workstation has a VPN connection to a given network (a client's, for instance) and an open connection, what determines how a request for a network resource (e.g. a web page) is routed? Moreover, given that a resource (e.g. google.com) could be available via either route (i.e. VPN or non-VPN), how is this route determined? Is there a way to 'force' the routing to use a given route or the route with lower overhead?
This depends on two things:
The only way to force a route, would be to add a static route to specific network to be through a specific router. Otherwise, your default route/gateway will be used.
depends on the VPN Client. If your VPN client is configured to allow split tunneling then traffic destined for an internet page will go out through your local internet connection. If it's a page internal to the VPN tunnel, then it will go through the vpn adapter.
If split tunneling is allowed then only internal desitnations are going to go through the VPN adapter.
By now you should have figured this out but yes you can choose to either allow or deny split tunneling.