Use ESP8266 as WiFi client connected to Arduino Pro Mini
Ditch the Pro Mini.  Upload your Arduino code to the ESP directly. There's a GitHub repo with the details. ESP for Arduino IDE has a ton of libraries. I'm sure you'll find it there. 

But if you're bent on using the Pro Mini,  you'll have to use AT commands over serial to control it or flash a custom firmware into the ESP using Lua or something. And Pro Mini can use its hardware serial just like a Uno does.