Maybe it is a kid, but it's just not her kid. It looks like the oldest son has a girlfriend, or at least he did around Halloween. Could be completely off course, but if this is all conjecture, it's definitely not out of the realm of possibility. Most things I've gathered from this point to this being an inside/domestic thing and not very well thought out. An angle worth exploring, but that's just my 2 cents.
I can also confirm that that block/path to the park is peppered with security cameras (private, municipal, and commercial). So unless this person covered their face the entire way, they're almost bound to have caught them in the act. If the NYPD has a positive id, they're probably not going to disseminate that information until the DA has time to build up the strongest case possible, and that takes a lot of subpoenas for phone records/ social media/banking records etc, interviews, and fact checking in a case like this. Even more so if it ends up the person is a minor.