I was wondering whether men and women killed their children in equal proportions because of mental illness and found this, which doesn't answer the question but seems interesting nonetheless:
Findings from most in-depth study into UK parents who kill their children
The over-representation of mental illness in filicide was the key finding of the study. Forty percent of filicide perpetrators had a recorded mental illness…
Overall, fathers were significantly more likely to kill their children than mothers, and were more likely to use violent methods of killing, have previous convictions for violent offences, perpetrate multiple killings, and have a history of substance misuse or dependence.
Could men receive less sympathy and women more because of the presence/absence of those factors?
I don't think she should be denied sympathy just because men are less likely to receive sympathy.