Could someone not report the death of their baby due to a deep trauma of losing that baby? In my story the father of the child comes back to find the mother and the child. Five years have gone by and the mother had changed her name and moved away. The mother lives with another mother who has a child the same age hers would have been (they met at the hospital when they were in labor). Both had been abandoned by their baby daddies and bonded. However, due to low to no income the mother loses her child but is deeply traumatized. Neither report it because they don't think about it. The reason being, I am wanting the father to go after the other woman's child because he thinks it's his own. Is this plausible?
Is Pauline in “Bodies” by Sex Pistols a Real Person? Did She Carry a Fetus in Her Bag? (naijaonpoint.com.ng) Is it plausible? Read this horror story from the Sex Pistols
You can make it plausible as long as plausible motivation is given. Rather than just having them "not think about it" (although that might be the case if they were drug addicts), it might be more believable to have them think about it and reject it, and make the reasons for the rejection believable. Are these characters irresponsible? Are they afraid of authority? Are they afraid of getting into trouble? What is their psychology?
They are not irresponsible, but very afraid of authority. They have been abandoned significant others (sperm donors). The MC mother has been betrayed by her family, disowned, and was shunned by all her friends. The doctors think she is a junkie because she is so thin and is a bit paranoid acting. They try to convince her to talk with social services or something of then like. The MC takes it as they think she is incompetent and want to steal the child All she has in life is that baby. She reluctantly becomes friends with the other mother who herself ran away from an abusive relationship. The first month is hard, freezing cold winter, no money, no food, no help. When the MC loses the baby she was sick and fevered. She goes a little crazy because she won't let go of the baby. Her friend talks her off the ledge, so to speak, and the MC only agrees to let the baby go if they can bury the baby in a forgotten part of a park. The MC doesn't trust anyone, doctors, police, anyone but her friend. So that is my reasoning for not reporting it. MC feels abandoned by people and society and doesn't want them interfering in her and her baby's lives, and death. Plus they don't have money for a real funeral.
It's not just plausible, but there are many accounts of this happening. Not so much in modern times due to better-kept records, but it has happened in the past. One possibility could be a child dying of SIDS and the mother was too afraid that suspicion might fall on her. This is especially possible in areas of the world where police are typically not trustworthy.
The mothers move a lot due to little to no money, so there is no one around to remember the baby. They finally settle in another town where they know no one. They are poor so authorities and most people overlook them.