The upside of having young children is always having a subject for pictures. The down side is finding time to take them. I'll try again this evening.
In the meantime, I've been reading and rereading a variety of articles at my favourite photography website, Digital Photography School. Some of the articles on composition have already helped I think.
In my first photo of my daughter, I worked with the rule of thirds to try and bring the attention of the viewer to her eyes, and I also tried to 'fill the frame' to make her face more striking.
In the photo of the paints, I tried to compose with a 'lower-left to upper-right diagonal' which is supposed to help draw the reader into the photo. I do like both pictures more than most I have taken, so I do suspect these rules are helping.
I doubt I have an readers at the moment, but I welcome any comments or criticism if you are out there!