I don't have an Ipad, but I can highly recommend a Kodak Zi8 to do what you want. You can get a used one for $100. or less: http://www.amazon.com/gp/offer-listing/B...ASIN=B002HOPUPC
In addition to the built-in mics, it has a stereo audio input. Just ran a cable from the keyboard or mixer at the same time you make the video.
If the Ipad has an audio input, then you could do the same thing with it.