That would be everyones dream point and shoot, but unfortunately you would need an DSLR with some good lens.
If you want a point and shoot:
-Movement in low lighting will be blurry
-Rapid fire is accessible but to a certain amount
Now you could buy a point and shoot with a hot shoe on top that can take an external flash, which would help out a lot.
I am looking to buy a new camera as I have pretty much used up my current one (I think that that last beach trip did it in). My current camera is a Sony Cybershot DSC-W1. I need a camera that I can use to keep up with my kids (ie can take rapid fire pix ???) and one that takes decent shots in a poorly lit auditorium. All of my kids are a bunch of hams and are always performing on the school stage. I have yet to get a decent picture of any of them. I am hoping to get it together for the next school year! Something that is fairly durable is useful as well. Thanks for helping.