However... using full auto mode for... say landscape photography, if lighting was a bit bad, the camera will automatically step up ISO value. However being a small sensor camera high ISO noise performance was definitely not something it excel in... and so you get photo that had lost details to noise. Secondly if you use auto for fast moving objects (eg. your baby). The shutter speed might not be there and instead the camera might be opening or closing the aperture only and so you still don't get the desirable image quality you wanted.
All I can say is... know the limits of your camera, then learn abit about the relationship between ISO, aperture and shutter speed, you will get better result. As to wanting your family to be able to use it, well... they can stick to Auto if they wanted, that is their problem. You do not have to do that. And let me share with you, I have a mom and a dad who are 60 plus, I gotten them a camera before and they quickly picked up simple photography techniques and stuff like that, now my dad could use aperture priority and shutter speed priority to achieve what he wanted.
Seriously I don't see the issue in that. And in my other comments in other thread addressed to you... you can buy a 5DmkIII, a Nikon D800, a Sony A95 etc, etc, and still get the same crap you have now, except these craps are sharper only.