But the Detectives should have known what they were dealing with, or at least had an idea. They deal with liars all the time, and if they are in homicide, they should be able to get a feel for a witness and use different techniques to interrogate, depending on the results they are getting, and they weren't getting results and don't appear to have changed tactics.
BTW, saying things to her like "how do you think lying to us is going to help us?" was counter-productive...allowed her an opportunity to explain many of her lies. They acted like they were questioning a scared child, when in fact they were probably questioning a cold blooded child killer (big difference). I just think they should have been able to change interrogation tactics and tried other ways of interrogating her.
There might be laws of interrogations that they need to follow to avoid evidence and statements being thrown out due to coersion, threats, etc.