As the child of a mother who beat me in a very similar manner to that in the video, I must say that I did not have children for that reason nor have any of my siblings had children. My mother had a terrible "temper" and I had bruises under my arms all the time. I have a "temper" that I must watch all the time. The doctor says these are related to female hormones, but I don't know.
Please help this little girl before she is scarred for life, if not physically then psychologically. The mother has her own issues and should be working on those rather than raising a child. I know from my friends who are parents that when you "loose it," you must step back and count to ten and count to ten again until you have calmed down enough to behave as a rational human being.
HITTING A CHILD IS NEVER RIGHT!