A normal parent, with normal emotions, would be expected to have had certain emotional reactions to the death/loss of a child, even if that parent caused the death/loss (either intentionally or accidentally). Although I accept that we do not know the details of what goes on behind the scenes of these parents' lives, the parts we have been exposed to show a significant lack of attachment to their baby. Even if one of them did purposely cause baby Deorr's death, if they had any attachment to him at all, there would be some obvious suffering around the loss of an intense and meaningful relationship. If they didn't cause his disappearance, there would be indicators of overwhelming grief, fear, desperation, loss, guilt, anger, loneliness, etc. No matter the circumstances, the death/loss of a young child is a debilitating blow to a normal parent.
Also disturbing is that if someone cannot attach to their own child, that person most certainly cannot truly attach to a friend or spouse. If I were in either of their lives, I would get out; without that option (if they were in my family for example), I would take drastic measures to protect myself from the constant threat of being hurt and humiliated. How incredibly lonely it would be in a relationship with someone who literally does not care about the other person at all. Lonely and, to be honest, terrifying.
This all being said, I think the only way JM will confess is with an opposite approach than what is happening now. I think she needs to feel like she was the real victim here; like someone understands how difficult her life has been, how whatever happened was absolutely beyond her control or, if done on purpose, was totally understandable. Someone must convince her that they know how terribly unfair things have been for her since this all happened and they deeply admire her ability to persevere in the face of overwhelming adversity. Poor Jessica; if only we could all be so brave.
In my opinion, JM doesn't care if someone is mad at her or if her behavior is torturing her family; without attachment to anyone else, she will not do anything out of compassion or guilt.
I think it's going to take a somewhat similar approach with VK. He might not require as much coddling, but I think he will respond best to someone who approaches him as the unassuming hero in this sordid tale. The person needs to convince VK that they recognize and appreciate that he had to do this, that and the other in order to protect JM, whose manipulative spell has only recently been broken. I mean, aw shucks, even though she rejected and embarrased him in front of the whole country, all DK still wants is JM to be happy. In my opinion, he will drop his defenses once everyone realizes he is just an honest and sweet-natured good-ole-boy with good intentions who naively left his son with a trusted adult.
All of this jabber is my humble opinion only.