Parents do not have the authority to simply override or exempt their child from the school's disciplinary processes. If there is a problem with a particular disciplinary action, such as detention scheduled to be served at a time that creates a hardship for the parent, you should contact the school's administrative staff to ask for consideration of an alternative date and time for the detention. But the schools cannot operate in an orderly or effective manner if some of the students are immune by parental pass from enforcement of the school's rules and regulations.
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You also should read the student handbook carefully. Many schools hand these out at the beginning of the year and have the parent and student sign a copy or an acknowledgement form.
If you can't find your copy see if one is available online and look to see if there is some kind of appeals process. If there is one, it is typically just within the school or district. Usually, there is no remedy beyond that point, sometimes you may appeal something to the school board. In the vast majority of instances I have seen, principals rubber stamp the decisions of their teachers and school boards rubber stamp the the decisions of their principals. Are there exceptions, sure, but in general you will find that how I described it above is how it goes.