Theory
Something happened either Sunday night or Monday while the boys were at school. Possibly, Dad was trying to sleep for his night shift and the baby just kept waking him. Either he or DB lost it and in a fit of rage fatally injured Baby Lisa. Then in a panic both JI and DB decide that they must not report this. They will lose both boys, if they do. So they come up with a plan.
They temporarily hide Lisa in the backyard. DB removes the clothes because they are soiled. One of them scopes out a good place to get rid of any evidence. They drive around and decide on the dumpster. One of them sees a kitten (if there ever was a kitten) and brings it home to keep the boys occupied and away from Lisa's room, The door is shut because, they tell the boys and the neighbor, that Lisa needs sleep. Mom sets up a movie time with the neighbor, again this keeps the boys occupied, and she asks her brother to take her to the store where she buys the biggest container of wine that she can find and things for the baby. She probably really does need a drink, now. But it is more for an alibi or reason she doesn't hear anyone break in. After the neighbor leaves, she stages the house...pushing in the screen, leaving the door unlocked and the phones are JI's afterthought. That way we can say that the intruder took the phones so we couldn't call 911. After that the dumpster is set on fire as a red herring to point to someone getting rid of evidence of the abduction & theft. At some point, right before JI drives home from work (2:38 AM) DB turns all the lights on in the house. DB turns the fan on high and makes sure that the baby monitor is turned on. Maybe younger son heard mom milling about or coming and going, woke up and got into her bed. I doubt that was part of the original plan. JI did ask her why the boy was in her bed. It's finally time to call 911. And then the inconsistencies begin to unravel.
At some point during the day, if no one other than a family member says they saw Lisa, then DB...maybe with the help of her brother took Lisa somewhere special to her and buried her. I doubt they are going to find the burial site. I still don't see anyone in that family dumping their baby.