I could be barking up the wrong tree, but if the aperture changes then the shot can change as it will change DOF. When on Av though, depth of field stays the same. I can see the need to increase ISO when trying to make sure that you freeze the action, I did this when taking a photograph of a bird. When it's pretty static though, raising the ISO on Av mode will produce the same level of exposure (not that I'm trying to restart that whole debate again) but with more noise. With children, you will want a fast shutter speed in order to catch them. Using a higher ISO would not have changed the amount of shadow in these shots, and they look like pretty static shots so I don't think that changing ISO would have helped. Using something to act as a reflector would have made a difference. It could be as simple as a large piece of white card and some baking foil.
To the OP I'd say: Take your time. Try and get one thing right at a time