2 Networks & 2 ISPs

I have a situation where I will have two neworks 10. & 192.168., the 10. will have a shared dial up connection to the internet and the 192.168 will have an ISDN using NAT. 6 of my workstations will be multihomed. My question is which connection will these 6 workstations use to access the internet? Will they automatically choose the first connection that responds (the ISDN I Assume) or do I need to do something to force them to choose. the reason for the dialup nework is we are running a prioprietary application which the vendor requires a VPN to their servers and they do not support ISDN for their connections. I do not want to slow my users down by forcing them over the dialup to access the web.