When you teach younger students, you'll find that sometimes their parents will want to sit in on their lessons; this can be helpful, because it gives the parents a better idea of how to help their child practice over the course of the week, but parental presence in the studio can undermine your authority if you aren't careful.
My number-one tip for this situation is to be clear with the parents about what their role will be if they choose to sit and observe. Parents are always welcome to sit and watch their child's lessons in my studio, but I do request that they refrain from chiming in with their own comments, because it can be confusing or distracting for the student.
One way I keep this from becoming an issue is through judicious studio setup. I make sure that the student is facing away from the parent but angled in such a way that the parent can still get a reasonable view of what's going on; this keeps shy kids from feeling self-conscious about being observed and allows the parent to feel somewhat included.
At the end of the day, it's up to you to set the boundaries in your own teaching space. By and large, families will respect whatever reasonable rules you set for your studio, and it's up to you to create an environment where everyone--parents, students, and yourself--is comfortable.