Not only would it be embarrassing, but it would also be a waste of time for a second mortal coil cultivator to run around investigating a death. Such a mission doesn't need their great strength.
It is unlikely that the murderer is a second mortal coil cultivator because they are rare, and such people won't lower themselves to kill a junior who also happens to be a member of the Dyson family.
Even if the murderer is a second mortal coil cultivator, the most the family will do is negotiate a fine. There is no way that they will ask for the life of a second mortal coil cultivator in exchange for the life of the first mortal coil child.
It is not that they can't. They can, but it will be a waste of their time because no matter what they do, they won't be able to bring back the child. Also, they will be offending a powerful person who has the chance to reach the third transformation for a dead child.
