The Little I know:
I know that there a children that have difficulty finding a Yeshiva or Bais Yaacov (to some extent this is simply a function of the opening of new classes not keeping up with population growth) and that there are children that are thrown out of Yeshivos all the time. What I haven’t heard of is a child being thrown out because the parents of other children insisted on it.
I cannot imagine a scenario other than immediate physical danger in which I would call my child’s school with such a demand. And I don’t know anyone else that would do it either. I therefore have a very hard time believing that this is a common thing.