I believe that you are correct. No one missed Tylee, aside from JJ. And the only people who missed JJ were the Woodcocks.
I really think that LVD missed a step. When the Woodcocks called the police for a "Welfare Check" on JJ, LVD could have easily gone on the defensive, and said that JJ is adopted, she is his legal Mother, and the Woodcocks need to stop bothering her, and her son. They have zero rights to any contact, and the police should not be used to harass law abiding citizens. That would have ended the inquiries dead.
When she fled to Hawaii, it got the police far more involved. And they followed up with the situation with CV in Arizona, BB in Utah...