You could try specifying the DNS servers in the “Ethernet” (or whatever connection you’re using) in the “Network” system preference pane. I haven’t tried this approach, but it my work. Other than that, you could give the Mac a static IP, thus specifying the correct router and alleviateing the problem.
However, it is generally a bad idea to have more than one DHCP server on a network, even if you have multiple subnets. It just allows for more confusion (for the machines). Given that, you should probably separate your IP phone network from your computer network. I’m guessing that aside from identifying the ports, you have a couple switches with ports connected through patch panels, so you could merely make one switch dedicated for your IP phones.