I'll not check the Ethernet library then 
Thanks for saving me a lot of time there.
It's a shame there's no function to add an IP address with its MAC too so it never has to try and get that info from the network. Obviously on Windows or Linux you can manually add a static ARP entry with the arp command.
On my router I can "isolate" any of its WiFi networks, which means all devices using that SSID have no access to the LAN and can only access the internet. This does work and would be a good solution but I need to access my LAN from wireless devices (e.g. VNC/Remote Desktop from my phone to PC).
Unless there's some undocumented arp command, it looks like I'll need a cheap router. There's another device that is (optionally) connected to my network that does this every second (another embedded system) so that sweetens the situation a bit.