Without looking at your specific situation, I can't be sure what the problem is. However, it sounds like a routing issue. For packets to go from one NIC to the other, the server needs to be able to act as a router. Depending on your server type, you might be able to set up this type of routing within the server. Or, you may be able to tell the VPN connection to use the other NIC as a the default gateway for the Internet. In any event, the problem is routing, and a network engineer should be able to look at your setup and figure out the correct settings.
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