Looking for a digital camera w/ double exposure?

To begin the reason as to why your flash flashes twice is not because it is actually exposing the image twice, no that would result in a double exposure. What the camera is doing is instead reducing the amount of red eye by causing the persons iris in their eye to shrink or get smaller thus preventing light to bounce back from the blood rich retina thus creating what we see in a photo as red eye. With the type of camera that you have the only way for you to make the flash less harsh is to buffer it with some sheer cloth or even say a tissue. This should diffuse the light somewhat although not to the degree a off mounted, swiveling flash or a flash with a custom diffuser would do. As for the fuzz, change the iso rating on your camera to a higher setting, perhaps 800 ISO. Sounds like the shutter speed is too slow for the ISO that you are using.