Were Lisa and Grady 'Elm Street' children/was Schneider part of the mob?

Since this whole movie is all about subjective interpretation, what do you think?

It seems like Freddy probably had his eyes on Lisa, Grady and Coach Schneider from the very beginning and all along was plotting to use Jesse to eventually get close enough to them. Lisa and Grady both seemed clueless about Freddy and the history/happenings of Elm Street, but the timeline, location and situation make it seem logical that their parents were part of Krueger's killing mob all those years before. Also Freddy specifically targeting Coach Schneider seemed very conspicuous. Freddy didn't usually make it his business to go after an adult who hadn't been part of his lynch mob.

So, here's my attempt to try and make this odd duck movie "fit" into the rest of the series and give it some logic, despite its many plot holes and inconsistencies. Grady's parents, Lisa's parents and the Coach were standing alongside the parents of Nancy, Tina, Glenn, Rod, the Dream Warrior kids that decade before all the dream killings started, torching Krueger after his mistrail.