I forgot to address this. Domestic violence against women has been taken very seriously here in the US for over three decades. And rightly so. Australia, The UK, and the US all have domestic violence shelters. Yes, it's tough to leave an abusive situation, but I have friends who have done so successfully.
Domestic violence of the type your wife experienced is not the only dynamic. Very often the woman is the initiator of physical violence. In cases where the violence is mutual (i.e., the man is retaliating/defending himself) the man will always be taken into custody. In cases where the woman is the sole perpetrator of the aggression, the police are not so eager to act, especially when the husband asks them not to (generally because they fear further retributive violence when the woman is released).
The three police visits to the house in response to domestic disturbances with no arrests made is typical of female-on-male violence. The knee-jerk reaction to this article (and to the issues of domestic violence in general) is "that poor woman". This is fine for melodrama and fairy tales, but real life is much more complex. Abuse flows in both directions, but the court system is biased against men if favor of "the weaker sex".
I was in an abusive relationship for several years. Or, if I were a woman it would have been considered abusive. I was abused fiscally and emotionally. In divorce and custody cases, a man can have a restraining order placed against him for shouting at his wife. This doesn't go both ways, however. My ex shouted at me constantly and at one point tried to provoke me into a more serious altercation while secretly videotaping me. Everyone who knew us as a couple thought my ex was horrible, everyone who didn't know us thought I had abandon her and was a terrible human being because the cultural narrative in domestic disputes generally casts the woman as the victim and the man as the perpetrator.
The article makes quite clear why she killed her husband. It was because of his affair.