Hello,
I'm a professional Systems Engineer and Developer, specialising in C++ based Windows application(and driver) design and development, targetting all versions of windows(up to Win 10).
Your functional requirements are best served using DirectX (C++ and COM technologies) and WMF(also C++ and COM) , both of which facilitate recording of webcam video stream, audio streams(built-in mic) and separate audio streams(using externa microphones or other audio devices).
I have worked with webcam video streams and audio streams, and Microphone audio streams, using DirectX and raw Win32 C++ APIs, for many years now, and can design and develop this application for you, with a high degree of confidence.
But, your budget is too low for Me, as I'm form the UK and 2,000 USD is 5 days wages for Me, and even at HALF that rate, it would still take 3 -4 weeks to develop this application, test it and deliver it, to professional /industry standards.
If interseted, let Me know.