Needs moar background info.
She could just be a shitty parent dragging her kid around (lulz wordplay) because she doesn't want to pay for a babysitter or whatever and sees the kid as a burden. She could also have the misfortune of having a shitty kid who doesn't know how to behave (which is partly a failure on her part -- some kids just plain refuse to behave and have to be trained like dogs; if that's the case, this kid isn't getting enough discipline to begin with), and she needs to get stuff done while also dragging the kid around (Woah, there it is again!) because the babysitter cancelled and her husband's at the office boning his secretary.
The former is horrible and indicative of an abusive home life as well, so I'd support the charges. The latter is still bad, but at least understandable and I don't think it warrants more than a misdemeanor. Seeing as the kid was on a leash in the first place, it's probably more or less one of those two.