Your Mac will send Internet packets to the top Interface listed on the System preferences > Network pane. Packets that are going to devices on the local Network are sent directly, not via your Router.
You may need to set Internet addresses very carefully to get Internet packets to go to the Router to get forwarded to the Internet, and local packets to go directly to local devices.
If you want help with this, list the Addresses you are using, and which interface is the topmost in the Network pane. These should all be "strictly-local" addresses, and not anything that is Internet accessible, so you will not be giving away anything private. (for example, lost of folks have 192.168.xxx.yyy addresses and/or 10.10.xxx.yyy addresses on their local networks, but they are not directly reachable from the Internet because they are in one of three "strictly local" ranges.)