and we don't know how picky you are. We also don't know how far away the stage is from "the back of the theater".
If there is good stage lighting, then there is no "low light" issue. But manual controls - specifically iris/aperture and exposure should be set rather than use the auto controls.
Assuming we go with the "low light" you mention, the *best* you could do would be is a camera with 70mm filter diameter lens (larger is better) and an imaging chip - preferably 3CCD (or 3MOS) - 1/3" (larger is better). There is no camcorder with these specifications in your price range. The closest I can get is the Sony HDR-FX7 (the lens falls short). The Sony HDR-FX1000 meets the requirement. Both use digital tape and can connect to external memory systems if needed.
The camcorders in this "prosumer" class have lens threads that allow addition of a lens - including wide angle.
You mention nothing of audio. What is your expectation?
I am looking for a recommendation on which digital video camera would give me the best quality taping musical theatre. Always taping in low light with changes in spot lights and light changes from dark to brighter. Alot of movement with dance. Also taping from the back of the theatre which would also make distance a factor. Are there any video cameras that would give me quality recording for under $1000 or do I have to move up to a professional camera. Are there any cameras that have wide angle lens capabilities?