The Touch can make a wired or wireless conection but not at the same time. The firmware would require a reconfiguration each time the method of connectivity changed. TouchToolbar2.0 can disable the wlan card but then it reboots leaving only the ethernet card working. By holding down the power button you can put it back to factory specs (both cards) but that requires reinstalling the TouchToolbar2.0 each time.
Essentially, you can do what you want but it will be a bit clumsy, and you sure will learn how to configure the Touch.
The mouse issues are probably caused by SqueezeBox Server utilizing the resources on the PC. Moving SBS to another PC will resolve that. Vortex Box is an OS, not an app, it will take over and its Linux, are you ready for that?
Larry