IMO, precisely because it was so early in the investigation, they would not have been looking for a suspect. A suspect for what? They didn't even know a crime had been committed! IMO, they would have been primarily looking for Christine herself, who, at that stage, could have very likely been a runaway.
If I were in the position of LE, I'd have interviewed HH as an observant, close friend of the family, in order to get an outsider's perspective on the family itself: each of the family members (are they reliable, how did they treat Christine, what kind of person was she, how did she behave around her family and strangers? ), and then also the circumstances of the whole situation (father in jail, etc). They probably interviewed her teachers, and the parents of her friends, and her friends, in case she had talked about somewhere she liked to go hide, etc.
Unfortunately, you can't just believe everything a mother says, you do need corroboration. And then, did HH have any facts or suspicions to share that might help the investigation. If she'd said "I noticed my husband leering at her, and he's acting weird, and I bet he abducted, raped, killed her and left her somewhere where she won't be found", you bet they'd have interviewed him.