Maybe Billie didn't call Shawn, as soon as she heard from DD, that Hailey did not spent the night with MB and that she was not at her dad's and she got that info from Shawn as to where Hailey was going to be, because her sub conscience, was not letting her go there.
She thought Shawn was work, we think, I would assume, not far from her, he had her car. We would think that logically, she would call him, verify for sure, that's where Hailey told him she would be. Let Shawn know what was going on.
I would think Shawn's employer would have let him leave, to pick up Billie and take her to the PD, to file a missing person report.
If Billie truly thought Shawn was at work, I believe she would have called him, either her sub conscience told her not to, or she already knew he he was not at work.