What is the religious ruling regarding a wife who killed her infant child unintentionally, and is expiation (kaffarah) obligatory for her in this case? And is the husband entitled to separate from her in this situation?

If the wife is not aware of what she is doing and kills her son, then there is no blame on her, and the blood money for the son is on her 'aqilah (male kin on the father's side responsible for paying blood money); because she is like one who is insane, and there is no qisas (retribution in kind) for the insane. However, if she is aware of what she is doing and killed him in the aforementioned manner, then qisas is not applied to her according to the majority of scholars, but rather blood money is incumbent upon her. This last assumption is unlikely.