Do school teachers demand more from their children than other students?
From Personal Experience, teachers will demand more from their child if their child is in that class for a couple of reasons: To show the rest of the class that there is no favoritism towards the child, as well as to ensure that the child performs exceptionally in the class.

Whether they achieve better/worse results is dependent on the level that this "extra demand" is taken to. For example a child may feel like he's being treated unfairly, and act out as a result, or become overwhelmed by the amount of work. But if it is a reasonable increase in demand, then the student will surely benefit.