Familiarize yourself with the actual play or the order of appearances. Read your child's script to get a feel for where the main action will be, and focus your camera there. Attend a rehearsal, if at all possible, to better prepare yourself for surprise entrances or sudden disappearances. What you are trying to avoid at all cost is the constant use of zoom while simultaneously sweeping the stage for any sign of your child. This is one of the most unpleasant effects to watch on a television screen, so do your homework first.
Cameramen have access.
If you are serious about professional results, think like a professional. Newspaper photographers are constantly scouting out the best place to get right into the action, without becoming part of the action. Don't feel obligated to sit in the back row of the theater and hope that the zoom option can find your little ant among all the other little ants. Get as close as you possibly can to the action, right up to the point of climbing onstage. People want to see facial expressions and costume details, not the standard panoramic scanning of the entire theater from the balcony.