One of three things happened.
1. She gave Gabriel away in spite of a custody order.
2. She sold Gabriel, in spite of a custody order.
3. She killed Gabriel.
If Gabriel is ever declared dead, she could be charged with his death. Most likely that would be a murder charge. If she sold Gabriel, that's illegal. She would be looking at serious jail time.
If she really gave the baby away, she could still claim that she had "good reason" or was mentally unstable and she would be talking, because recovering the child is her "get out of jail relatively free card." She would face custodial interference, kidnapping, and contempt of court, but if she were convicted, she wouldn't get a life sentence--and her attorneys could bargain for the best deal, given her cover story.
Clearly, she can't talk if she killed Gabriel. And if she sold him--well, that destroys the facade that she was "doing the best thing for her child." Even in the sick world of illegal adoptions, it's hard to argue that a person who sells a child to a stranger has his or her best interest at heart. If she sold him, she would not only face major jail time, but also the loss of her facade of righteousness and her sense of self (however twisted that we find it) that allows her to justify what she does and feel OK. That's what she's crying about: being in court in front of Logan and other witnesses threatens her self-identity. It would come out that she did it for the money. or that she is a murderer. Whatever she tells herself about what she's done, people holding her accountable in a place she can't escape, in front of the person she has most wronged (other than Gabriel) is an intolerable assault on the "self" that she has constructed. A psychologist once told me (in response to a question about why people lie) that people lie to protect their sense of who they are. Now she can't tell her "gave the baby away" lie, either on the stand or off, because she'd have to cough up names, places, details that can be exposed for the lies that they are. (Brings to mind the Zenaida Gonzalez mess that Casey Anthony made for herself.) And now she knows the lie won't make her most basic problem, incarceration, go away. She can't talk because she can't tell the truth and the lie no longer gets her anywhere.
So if you think she wants to "talk," no doubt she has a strong urge to make up a load of crapola to rebuild her battered sense of self and to get people to go, "Oh, OK. You gave the baby away because this father who is turning the world upside down to find his son is UNFIT. You get to go free! You did a good thing! He's the devil!" But her lawyer knows that's not going to happen so she has to sit there and take it. Hence the tears. She can't make this problem go away or Logan go away or the judge go away or the consequences of what she did go away.
I still think she sold Gabriel, so the best hope for him and Logan is the PI finding him in the home of someone desperate enough for a baby to buy one.