This is not "news". Nor is this limited to mothers, or even females. It is well established that people suffering from depression can have more extreme reactions to stress than those who are not.
The specific study is not cited, however, I can make an educated guess, based on the comment regarding "ones is poverty" (which I assume is versus those with a middle class income or higher) being "less reactive", and say that this was a study about situational depression and stress. Situational depression is that which is caused by negative events, or those perceived as negative, in a person's environment, lifestyle or finances...for example. Persons with higher expectations and a higher constant degree of comfort who suffer a tragedy, a financial loss, loss of employment, serious illness or any real or perceived negative have a much more difficult time coping with their new situation. This is usually due to to a lack of experience, no need to develop coping skills in the past, a sense that it "can't happen to me", a much higher level of security on many levels, and generally higher expectations for themselves and theirs. All of this can actually lead to situational depression, because the person can neither understand, accept, or cope with a sudden change of fortune. Once the person who has no coping skills or resilience becomes depressed, they often also become resentful, angry and enter fully into denial of their own culpability (if any, and there often is...women, even mothers, aren't saints) or ability to take charge. Their resentment has to be directed somewhere...and children are a convenient, silent, helpless target for their stress and rage. Men do it too...well off men who kill their own children or entire family.
Women who have always lived in poverty often have to learn the skills to cope with disappointment, huge absences in their lives, spouses who are away for long periods of time working seasonal or long-shift jobs (oil workers, lumber men, miners, etc., whose jobs are often by no means permanent), no insurance, poor living conditions, a lack of even basics like food and medical care. Yes, there are cultural elements among the poor who do not cope at all, ride the welfare system, and engage in an onerous lifestyle...but they are specific and I am speaking in general. If such a woman is depressed, it's simply a part of life to deal with, and she moves along. If such a woman has one more stressful thing happen, she is much more likely to roll with it, and move ahead with her life. Curiously, it is also a certain ethnic segment of the poor which sees most of the male family murder/suicides, which is culturally based in a firm belief that only a man can take care of HIS family, and he cannot allow another to ever fill his shoes...they would be better off dead.
I have been diagnosed with bi-polar I, clinical depression (yes, they are possible at the same time), OCD, unspecified anxiety disorder, and schizophrenia. I am medicated, and in control of my illness. I am not mentally ill. I do know what it is like to be depressed when poor, and when comfortable...but poverty came first, which taught me to cope more easily. I've never struck or abused my children because of my illnesses...but I understand how it could happen...because my mother, an alcoholic and an upper-middle-class woman all of her life, severely emotionally and verbally abused me until, and even after, I left her home. There is no excuse for anyone to abuse their children...father or mother, depression, stress or not. You bring them into this world helpless and dependent...and it is your responsibility to be accountable for yourself, and responsible to them...no matter what life hands you. Even the severely depressed can still think enough to get help. I'm schizophrenic and I know that. Yes, our mental health system is a horror show...but that is no excuse for victimizing children. Find a way.