While I agree that, without Tylee around, she would have to actually care for him and I highly doubt she was ever interested in being a mother to JJ, registering him in school still doesn't make much sense to me. That, added to the fact that she allowed him to play with a kid that lived near them is just weird. If the plan was to off Tylee and JJ all along, then not letting them be seen would make more sense, I feel like
@nhmemorymaker makes a good point: she let several strangers met JJ and that was super unnecessary. The fact that they most likely weren't killed at the same time also makes no sense. It looks like Tylee was the first to go, but I highly doubt JJ never asked about her and where she was, even though the poor child would just believe anything his poor excuse for a mother would tell him. JJ could never be the first one to go because Tylee would become a problem.
Even though JJ was probably easy to lie to, because he truly believed his dad was alive and just traveling, you never know how a kid is going to behave. Kids are umpredictable and, sometimes, say some interesting things. I can't imagine why she would take the risk of him saying something at school that would bring attention to the fact that Tylee was nowhere to be found.
I wonder if JJ and Tylee even met Chad or knew about him.