I am prior Military. I was a Behavior Science Specialist, I worked in Psy Ops. I'm certainly not a leading expert on human behavior, but I am willing to bet that allowing PF to bring his daughter was a very calculated move. If I were interrogating PF I would definitely do these two things...
First and foremost I would ensure leverage. In this case I believe the child is LE's leverage. Mind you, (regarding your question) the child is currently in a very safe environment.
Questioning AFTER the search warrant was implemented may suggest to PF that LE has found something that may strengthen their case against him (should there be one). LE can also say (whether or not they do or they don't) that they now have a strong case against him. This may ultimately get him to talk...