iPad Mirroring to PC (or Mac)

I have been tasked with developing a series of short videos that show how to use one of my company's iPad applications. While I thought this would be a simple setup, it is proving more complicated than I imagined. I tried using a program called "Reflector" on my PC. This, in theory, would allow me to use Airplay to stream the iPad screen to the PC. Unfortunately this is not working, as the "Airplay" button in the iPad control panel is not showing up. I also have a Mac. I tried connecting the iPad (iOS 8.1.3) via lightening cable and recording the screen via Quicktime. While this solution does work, it is too laggy to create a quality video. It also seems to lose connection to the iPad quite often. 

Has anyone else found a workable solution to this problem. If so I'd love to hear it. Thanks for your help!!