Dual WiFi network cards route outgoing traffic to specific cards
This would probably be a lot of work for people that don’t set up networks for a living, but let’s assume you have a good reason and propose a solution.

You would need to serve two networks so that each AirPort connects to a different network segment so each could have different routing or different DNS. All the setup would be on the network side and you wouldn’t really need to do anything other than set up DHCP on each wireless adapter and possibly set up a hosts file over-ride or tunnel traffic to onlybeta.com through a server / gateway on the network for the beta wireless card.