I have a theory. I don't know if I thought of it or I read hints of it elsewhere. But it's based on the weird things the parents say, and the way they speak. And on the old saying "there's an ounce of truth in every lie."
Hypothetical scenario:
Jeremy is a control freak with anger issues (I pulled that out of the air, but it could be). He goes to work. When? We strangely have never heard a word about this. Anyway, he goes to work.
Deborah goes to bed as she said. Her son comes into her room sometime after she goes to bed, and wants to sleep with her. She says ok. She "likes to sleep with" her boy(s) (she said this in one of the interviews in an awkward moment, but someone, either Jeremy or Jeanine Pirro cut her off as she said it).
Jeremy comes home. Not at 3:30 or 4, but some time before, like around 2AM. Maybe he's trying to catch her in the act of fooling around; maybe he just finished work early, maybe he was actually scheduled to come home and did. We don't know anything other than what he has said about him being at work. No employer or fellow employees have corroborated this.
So Jeremy comes home. He goes into the parent's bedroom and sees Deborah's son in bed with her. This is not allowed. He says (as she has stated in interviews) "why is he in bed with you?" but the context is not what they represented to the media. He is enraged for that and/or some other reason (wine was left out, and he's ticked off that she partied while he worked, jealousy, who knows?).
Somehow, in his anger, he harms the baby. Or accuses Deborah of being an unfit mother and says he's taking the kid to punish her. Whether he has already harmed Lisa in the house, or he hurts her later, he leaves with her. And he takes all the phones. But he calls her (on the landline?) or someone else (or texts) at around 2:30, which is when this is going on (that's if the phone call rumor is true). He goes to the river and that's where the phones and the baby's body are left. (I can't even stand to type this.)
This would explain why the odd statement and contradiction about the boy being in bed with Deborah was part of the media statement. Because it was significant (i.e., triggers his anger), but they screw up when trying to describe the events of the night - their stories don't quite synch (he went to check on the "boys" but one of the boys was right there in bed with Deborah).
And now Deborah is covering for him. Why? If he is an abuser, he may have threatened to hurt her or her son. She keeps referring to "the boys need her back...we need her back" but she never personalizes these statements to say "I want my baby back" because that's not allowed. It will cross Jeremy for her to voice disapproval at whatever he has done.
And LE somehow knows this. But they know Jeremy is cold and won't crack, so they target in on Deborah, give her a lie detector to try to get her to break and tell what she knows about Jeremy, and she does fail, because she is afraid to tell the truth. They think she's an easier target to break, so they are working on her. And that would explain her weird behavior of looking at Jeremy when she speaks (checking with him constantly to see if she's saying the right thing), and it would also explain her tearful episodes.
This could also explain her slip-up when she said "whenever we...whenever I woke up..." during one of the early media appearances. That struck me as so odd, like she caught herself saying something that did not fit with the story they were portraying. When Jeremy returned from the river, they may have gone to sleep until it was the appropriate "time" for Jeremy to come home from his shift, at which time they enacted their story as they told it to the media, pushing the screen out and calling 911..
This would assume that Jeremy's presence at work (continuously) until 3:30AM has not/cannot be corroborated. But isn't it odd that no one has spoken of when he left for work, nor verified his actual presence at work? If I missed that, forget this theory!
I can't come up with how the boys fit into this, except to note that Jeremy said in one of the interviews "the boys are sound sleepers."
I feel bad sharing this theory if it's off base, because it's the opposite of what I felt initially. But it would explain LE's continued focus on Deborah - trying to get her to crack. Then again, Jeremy could be Deborah's dupe.
Anyway, that's the theory.
This case is making me rethink (and change) my carefree ways. 
