The mom said LE kept pushing her because she couldn't fill in gaps in the timeline. They should have been pushing her, imo. From what is known so far, she saw Lisa at 10:30 p.m. Dad came home at 4 a.m. and Lisa was gone. Mom was sleeping that whole time, as presumably were the two boys. If that's true, there's your answer - no gaps. Possibly LE is questioning her about what went on earlier in the day to get more information or they have in fact gotten phone records and there was activity during this time frame when she claims she was asleep. Or maybe they have solid verified information about some things that took place leading up to the reported disappearance and the parents are not offering the information or denying it. We don't know, but the mom herself admits she was unable to fill in gaps.
If there are gaps in her account, that's concerning, imo. I see no reason for gaps if she was being asked about events that occured that day, that night, or in the days leading up to and following the reported disappearance (no drugs known at this point and the reported disappearance is very recent).
This isn't meant to conclude that mom and/or dad is involved, just that it sounds to me that there is good reason for LE to keep pushing the parents if they can't get the timeline pinned down. That's critical - what happened when. How does LE keep investigating without that foundation? I don't believe that the dad said "I need a break for today" after 11 hours and LE interpreted that to mean no further cooperation and alerted the media. That doesn't make sense. Not a pissing match, imo. The parents are trying to get in front of something (may or may not be related to Lisa's disappearance). Why did the parents realease the cell phone information to the public? Releasing that info doesn't assist the public in the search for Lisa and LE chose not to disclose it. They wanted/needed the public to know that their cell phones were stolen with the baby. Why? There is a reason, imo. Not sure what that reason might be and not saying it implies involvement by the parents, but there is a reason.
MOO.