I don't think the SD1000 photo's inherently any darker than the G6 shot. Look at the window shade - it's blown out in the SD1000 shot and not in the G6 shot. Granted the little girl's darker, but that's not necessarily an indication of an underexposed photo, given the blown-out window. It may reflect differences in how the cameras meter. Were the cameras in the same metering mode? What were the exposure settings used for the two shots? Since you merged the two photos into a single JPEG, I can't read the EXIF data for the shots. They're also a bit small. If you were to separately post (attach them to your post; max. dimension of 800 pixels in the longest dimension and not over 100 KB) them it'd be easier for us to assess them.
Have you looked at how you've set the contrast processing in the two cameras? Since the G6 is showing more detail in the shades and also a better exposure on the little girl than the SD100, it looks like it's set to a lower contrast value than the SD1000 can provide. That's something you can't change in the SD1000, AFAIK, which is not unexpected since the SD line is a "basic" camera with minimal controls for the user to use (and misuse) while the G6 is the culmination of the non-DSLR "Advanced Amateur" cameras with many and flexible controls that you're expected to know how to use before you monkey with them. If your wife's been using the G6 for any length of time, she's probably gotten very comfortable with it and has made adjustments from the default settings.
In short, I think there are a number of things that can be controlled which may be affecting the different appearance of the two shots. If your wife really wants a G6 but in a smaller package, though, I think she needs to look at an A630 or A640. The SD series are small, but they're designed for the family vacationer who doesn't want to be bothered with learning the camera. Notice, for example, that it doesn't even have a mode where the user can set shutter speed, aperture, or both. It's a good camera. It's just not a "control freak" camera. I got my wife an SD600 (predecessor) as her first "real" camera (previously, she'd picked up a drug store single-use one if she wanted to take pictures) as she's one of the "vacationer who can't be bothered" types. I use the A620 as my "everywhere" camera. It's usually on "P", but it has the controls when I need them. That's the difference between the SD line and the A line.