I like the second picture a lot. There are a few things to notice there for you to think about. See how everything closest to you and centered is in focus, and the rest is quickly out of focus? That has to do with a lens attribute called "depth of field". It refers to how much will be in focus beyond what you're focusing on. You can use this to emphasize part of the image by making sure unimportant bits are out of focus.
I don't know how much control that particular camera lets you have, though. Generally, the closer you are to something, the shallower your depth of field is going to be. You can fix this by adding more light, if possible. Or you can make it worse by removing light. Details about aperatures (f-stops) on request.
I agree that candid shots are better. It makes it hard to take pictures of small children, 'cause they can get to a point where they see a camera, stop what they're doing, and pay attention to the camera.
