Mothers don't murder their kids at higher rates, and the reasons why men and women kill children are different: women are more likely to kill through neglect, to commit infanticide due to an unwanted pregnancy, to be suffering psychosis, or to misguidedly believe it's to help the child in some way.
Men kill for far different reasons related to power, control, and entitlement
https://theconversation.com/men-and-women-kill-their-children-in-roughly-equal-numbers-and-we-need-to-understand-why-153527
"Research indicates that gender does, in fact, play a role in the type of crime committed and the motivations behind it.
Accidental killings of children, for instance, are more likely to be the result of neglect among mothers and abuse among fathers and stepfathers. This reflects what we know about gender patterns in childcare responsibility and domestic and family violence.
In cases where children are killed intentionally, women are more likely to kill babies and newborns, particularly in circumstances of unwanted pregnancies. Such offenders are more likely to be young and have low levels of social support, although it is increasingly reported among older women.
Mothers are also more likely to kill their children during a psychotic episode.
...
Women are also more likely to kill children out of a warped belief they are sparing them pain – for instance, of losing a parent to suicide."