First of all, I've gotta say 'thumbs up!' to your parents on their choice of names! ;)
As for your question, I'm assuming that by "the law of reflection" that you mean Snell's Law, where light bounces off a flat mirror at the same angle that it hits it at, that is if it comes in at right angles to the surface it bounces off the same way. If it comes in at say 30° from the surface it bounces off at 30° from the surface.
And the answer is, yes! Curved mirrors like convex and concave mirrors do follow this law. Or at least they do in a way... this happens when you make a certain approximation - that if you zoom in really really close on a curved mirror, it's basically flat. In math terms, this is saying that a curved surface is "locally linear". It's kind of like this:
(see pictures in follow-up)
So why do we care if a curved mirror is basically flat when you look really closely? Well, if you think about a single ray of light hitting the mirror, it only hits a very very small spot. And if we think of each little spot on the mirror as being basically flat, then each ray of light that hits the mirror acts like it's hitting a flat mirror.
When we draw light rays on a piece of paper, we usually use something called a 'tangent line'. This is just a straight line, drawn right up against the curve of the mirror. A tangent line is kind of like what the curve would look like really really close up. This way we can use Snell's law to solve problems with curved mirrors:
(published on 10/22/2007)