I don't understand what the problem is? they didn't arrest her, there was likely a bench warrant issued for her arrest (which means she would only be arrested if the police stopped her in connection with another offense). she turned herself in, was promptly released without need to post bail, and will no doubt appear before a judge and be assessed a fine as penalty for her presumably minor son exceeding the absence limit for school.
I suspect in Switzerland, as in many other countries, the mother simply would have been assessed a fine. for better or worse, however, in the US a fine cannot be assessed without "due process", meaning the mother must be granted a hearing before a judge before the state can issue a fine. in most cases, she could have waived the right to a hearing, plead guilty and simply paid the fine, but she opted for the publicity instead.
P.S. interesting that the article never bothers to mention why her child missed that much school.