You are describing a circumstance that does happen in certain communities, and as you indicated would depend on the protocols of the school district.  Now that you find your child in this situation, it sounds like you are wary of what might transpire. While you imply that the teacher may have had some pull with the principal, you have not said directly that anything unfair has actually occurred. However, it is reasonable for you to wonder if the teacher's own child will be the "pet" at the expense of the other children.

Here are my opinions.

Since it sounds like you are unable to change the situation, perhaps a change in perspective might help you. The fact that this looks unfair does not necessarily mean it will be unfair.  Rather than assume this will be a negative for your daughter, you might consider the possibility that the teacher will be more conscientious and more invested in the success of her class since her own child is a student there.  You might also adopt the philosophy that, as a professional, the teacher subscribes to a policy of fairness for all her students.

Along with choosing a belief system, one helpful strategy might be to develop an alliance with this teacher. Offer to volunteer in her class or participate in a Parent/Teacher activity with her. Get to know her so that you can form more than a circumstantial evaluation of how she is handling this situation.  A working relationship can go far toward mitigating or heading off problematic situations.

Now, if you do discover concrete, factual information that conflicts with the positive outlooks, create a documentation of evidence that you can  present to the powers in the district, if you feel the matter is sufficiently problematic. Bear in mind that your own child's complaints about fairness or lack of it, may not fully constitute fact, since a child's perception is often that adults are not fair.  On the other hand, what your child says is worthy of your attention, and possibly  follow up with the teacher, or with the principal, in a non-confrontational manner.

Above all, help your daughter to deal with her own feelings about the teacher's child being in her class. Help her to understand that despite this situation,  she is just as important as anyone else in the room.  Most parents work, and this is the job that this little girl's Mom has.  Because this girl is in your little girl's class, perhaps a play date is in order.  

In the interest of positive alliances, I would also encourage you to refrain from  sharing your concerns or frustrations within earshot of your daughter.  Doing so could raise anxiety for your child, or lead to information being "leaked" that you would prefer to keep private. In other words, make sure your daughter is not in the middle of any issues you have with her teacher.

To sum up, keep your outlook positive, find ways to be an ally as well as an advocate, and help your daughter keep her own self-esteem intact.  These positive practices will go far to mitigate any negative effects of potential "nepotism" in the classroom.

Bette J. Freedson, LICSW, LCSW, CGP