maybe op is just dumb but the article clearly says she was arrested for not watching her children
According to the woman arrested she was nearby in a lawn-chair well within sight constantly.
I don't know how true her claims are, since obviously there is bias in the reports on the side of the mother.
But, the charges were dropped, presumably because she did nothing wrong.
There's also the apparent lack of tact with the situation. It would seem they just immediately arrested her and took her children into custody, seemingly without much conversation between the mother and the police.
I don't know what the laws or police regulations are where she is, but where I live a police officer can only arrest if they absolutely need to.
Which generally means to prevent them from getting away with their crime, altering/removing evidence, harming themselves or witnesses or if they're unlikely to turn up to court.
In this scenario, if a mother is apparantely on the scene, but she's not near enough with her children, then it would make more sense for a police officer to turn up, talk to the mother and ask her to keep her children closer. As far as I am aware, with my limited sources, there was no need for arresting the mother and detaining her.