How to use WiFi and Ethernet at the same time
The solution was extremely simple.


Prioritize ethernet to be first.
Under System Preferences->Network Settings: where EN0 is Manually configured, leave the router field blank.


I thought the router field was required, so I filled it in. My Ethernet connection has a "router" per say, but it is not used to access general connections. By filling in that field, the Mac OS would automatically try to create a default route through the Ethernet NIC. This would redirect all miscellaneous traffic through the wrong router.

I also tried to delete this route in the routing tables before I found the solution to my problem. This would delete the route appropriately and allow the my software system to run correctly. However after around a minute or so, the route was re-added (as I later discovered) by the operating system. After the route was re-added the connections would fail, so I had to restart the process all over again. This fix proved to be unproductive.

I hope this helps someone with their networking issues.