The reason you are having problems finding such a camera is because no one has built one yet.
Zoom while using video - There are only about 5 cameras that will do that.
And with 4 of those 5, the microphone will pick up the noise of the zoom motor and you will hear the motor when you play the video.
The one with a silent zoom motor is rather large and has lots of things to learn.
Good pictures in low light - As long as you use flash, most digital cameras can do this.
If you want good pictures in low light without flash - none of the small/inexpensive digital cameras can do that.
Red Eye - All small digital cameras are susceptible to red-eye.
Red Eye preventive flash works some times but may result in people shutting their eyes during the shot.
Some cameras have Red Eye removal built into the camera, that seems to be the best solution.
View Finder - Very few small cameras have viewfinders.
Some of the Canon SD series have viewfinders.
All of the Sony W series have viewfinders.
And that is it.
5. Great Zoom - lots of camera with great zoom but they are not compact cameras.
One exception - The Panasonic TZ5 is compact with 10X zoom.
Can anyone help, there are so many and they have too many features.
I am looking for a point and shoot camera, compact size, no manual controls, really simple but with a GREAT ZOOM. I want really nice looking pictures of my children both outdoors and indoors. So low light and white balance and colors can be an issue.
Zoom available when shooting short videos ( 2/3 minutes )
I need red eye control, image stab, if possible view finder, video out, usb, etc.
The problem seems to be that when they have this it comes bundled with lots of other features which I don't need and which not only makes very expensive but demands that I dedicate to it more time then I have.