She laughs because it isn't just William who makes her laugh
As a mother herself, Kate Middleton is well aware that children can be quite amusing at times. Kate would have thought it was amusing that the kid on the right was attempting to eat her cup rather than drink from it. The Princess of Wales participates in various children's organizations and conducts a lot of charitable work. We can see her here, surrounded by some of the wonderful youngsters with whom she works. It's clear that she's having a good time in this one. Her face is shining, and she is using every muscle in her body to keep from crying.
Driving in Style
This is hardly the expression you'd expect from someone wearing a diamond-studded tiara, riding in a magnificent Bentley, and sitting next to, no, married to, a prince! This is what makes this shot so beautiful. Kate doesn't appear to be in a good mood here. In fact, she has the classic “you know what you did” expression on her face, and given how uncomfortable William appears to be here, he undoubtedly does. The two are cruising about in one of the world's most costly luxury vehicles, almost as if they are on their way to the prom, where they will be proclaimed prom king and queen.