Do school teachers demand more from their children than other students? Lets assume that there is a group of students and one teacher (typical school situation). 

Child of the teacher is in that group.

Is there any evidence, that school teachers demand more from their children than other children?

Is there any evidence, that children who are taught by parent-teacher achieve better/worse results than other students in same group?
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.