Aperture Priority and AF Controls
You're hooked! I like it :D
Your lens aperture - the size of the opening - not only controls how much light reaches the sensor, it also controls the depth-of-field. You probably don't notice the drastic changes in aperture when you change lighting situations because you just don't understand the aperture as much. But it will change just as much as the shutter speed when you're in aperture priority mode. They both have to compensate for the same amount of light.
I use aperture priority when I am concerned with depth-of-field. For portraits I like a very shallow depth-of-field and I'll try to keep the aperture at about f/2.8. For landscape, lots of depth is usually desirable. So you might want to use an aperture of f/11, f/22 or smaller. The larger the number, the smaller the aperture (size of the lens opening). A larger aperture will also give you a faster shutter speed since it's allowing more light to reach the sensor. Is it making more sense now?
One of the obvious weaknesses of most non-pro digital cameras is the AF. People who have kids often have a very hard time with this. The 828 has continuous autofocus although I don't know how well it works. I never tried it while I had the 828. All of the mountain bike shots I did were prefocused. Try the continuous autofocus with your kids and if that doesn't work, try to pre-focus. I wouldn't bother trying to use the manual focus. That's just not going to work.