CBT skill-deployment is pretty much worthless if the person is already in fight or flight. If you have been raised in an unsafe family, even good things like interpersonal intimacy can put you in fight or flight ("I better not trust this-- it will blow up in my face"). If you have been abused as a child then the natural naughtiness of a normal kid might be triggering because you possess no model to deal with it normally or calmly.
Dr Allan Schore (UCLA neuroscientist) says that in the first 2-3 years, "The right brain of the mother becomes the right brain of the child." It is the mother's right brain skill set (of self modulation, insight into the baby's feeling states, empathy, helping the baby calm down or perk up.) Providing this help is "external co regulation." From experiencing the patterning of how our Mom helps us feel better, we gradually learn how to help OURSELVES feel better (emotional self regulation).
So, you do need to help the parents learn how to mirror the baby and read the baby and respond to the baby from a calm, empathic place.
The good news is that you can teach a mother to 'mother' better -- through modeling / information. A la Nurse-Family partnership. And if you can support breastfeeding, it reinforces that dyadic care.