Two things to try, depending on how "candid" your subject is:
Tap the screen in the center of your subject matter (i.e. tap on your baby's face) to have the camera make that it's center of focus. Long press on the subject, and it will adjust focus and exposure. This may not always be feasible with moving subjects like a child, so the next option may help.
When you're in Auto mode, try using "burst" shots to help with the blur. Hold down the button when you take a picture, or hold down the volume keys (same function, different button) and it will take up to 30 photos in a burst. The faster shutter speed of the burst should take care of the blur of moving babies. You have to sort through a series of photos to find a keeper, (or you have a series to build a nice animated sequence with) but I have found this usually results in a much better finished photo than trying to point and shoot my way to one good photo--at least with moving subjects.