Programmable routers communicate with PC

[dilettante]

I doubt access point firmware normally provides any API for this, though custom firmware might do it via a Telnet/TCP connection or perhaps a Web Service.

More likely to accomplish this you'd use WiFi adapters and the related API. But even this would probably only support "ad hoc" networking and not normal access point operation. I suspect that requires different low-level software and drivers not normally part of Windows. At a minimum you'd want to configure Internet Connection Sharing in order to get bridging and routing within Windows, which might be enough.