It's a tough call.
Make sure you've got your audio set at 48/16bit in the camcorder.
Why not rent or borrow a good microphone like a Rode VideoMic or Sennheiser ME66/K6 (power module included--WARNING! NOT CHEAP!) and try that. Syncing the sound is a pretty joyless task every time you make a recording. Use manual audio controls on the camcorder and aim for -12db peaks.
I think you would get somewhat better audio from a separate recorder but, frankly, the edit process would wear me down after a couple dozen syncs. One of the unfortunate disadvantages of a flash memory camera is that there is no "automatic archive" on tape. You've got to store multi-gigabyte sessions digitally. This may also influence your decision since you are going to dealing with that anyway and a digital audio recorder isn't going to make much difference.
This is really a challenging mission you are on, Techgui. The difference between a "recital with piano" and "club band" is HUGE. With the former, I could be happy with either solution, but when I get to the latter, the club scene, I'm hoping to take a line output from the mixing board. That tends to favor the separate audio recorder, IMHO.
Good Luck to you...and your daughter!