This is going to be a long post. I apologise in advance but I really want to help people understand what abuse does to your mindset.
I left my abusive partner on the first incidence of physical violence against me (when my DTs were 4 months old). The only time my abusive XP laid a finger on my DC was after I'd already left him, at which point I kicked him out of my house there and then, contacted social services immediately and established supervised contact only. I was the primary earner in the relationship when we were together so had more advantages than most when I left him (I was made homeless but had the means to buy a home, for example). As far as the outside world was concerned, I was the exact opposite of what an abused woman is like. I did everything that people on this thread think a woman should do when faced with an abusive partner or someone who hurts their DC.
Despite this, I can still see why so many women don't leave and why some go so far as to let their children be abused. I'm not making excuses for it, but I just don't think you can understand it unless you've been there.
For me, the saving grace was the wonderful example I was set by my own parents. As soon as things became physical, I knew I had to leave. There was simply no way - no matter how much of an angle he or I tried to put on it - that I could find a way to excuse that. But other abusive behaviour isn't that straightforward. I look back now and I cringe at some of the behaviours that my X exhibited toward me and the excuses that he or I made about them so that I didn't feel I had to leave there and then.
The psychological abuse started when I was pregnant (as is often the case). No abuse of any kind in the five years preceding this, though with hindsight I can see behaviours towards others that should have raised concerns. That said, I can just imagine people's reactions if I posted a thread saying "DP got into a silly fight in the pub and beat the guy up. Should I leave?" I guarantee that as soon as the words "he's never laid a finger on me" were said, most posters would say that I would be mad to leave him based on that example. Abuse is a pattern of behaviour. You can only see it for what it is when you look at the bigger picture, and when you're in the relationship you often can't, especially when each isolated incident can be excused by itself very plausibly indeed.
Women in abusive relationships suffer from massive cognitive dissonance. They have a great deal invested in making excuses for behaviour. So the overly harsh criticism, or the jealousy because you were talking to another man, or the refusal to help around the home become excused because he was having a bad day, or he loves me so passionately, or he can't help it he's just a typical man and doesn't see dirt. These things are not so far removed from what goes on in many 'normal' relationships are they?.
Abuse just ramps it up, step by step, until by the time the first punch is thrown, you believe the justification presented by your abuser. Indeed, if he's that good, he won't even have to make it because you'll already be blaming yourself for provoking him. Even if you make a stand over it, if you accept his apology and try again, you've drawn your line in the sand so far from your original stance that you may as well have scrubbed it out completely. THat's why I get so frustrated with the some posters who blame women for not leaving and protecting children when they are very often the same ones who come out with trite sayings like "every one deserves a second chance" or "it takes two to make a relationship fail" or "be honest now, did you provoke him in any way?" or "if he's genuinely sorry I don't see why you can't put this behind you especially as you've admitted that you were partly to blame".
By the time you've reached this mindset, it really isn't that much of a stretch to believe that if smacking is acceptable in law and the child has been really badly behaved, then physical abuse of the child is ok. As long as nothing is broken it can't be that bad. Especially as the abuser will be claiming that the child is over-reacting on purpose and by accepting that explanation you can shield yourself from the possibility of becoming homeless, fleeing to refuge, having no money, no prospects, being scared, etc.
It's all an exercise in desensitisation. One tiny little chip at a time. The scary thing is, as psychological research shows, it can happen to any of us under the right circumstances no matter how strong our personal moral code. Some women grow up seeing abusive relationships as normal (either their own parents or by watching abuse in families in their community where other adults stand by and do nothing). Others grow up assimilating the culture that relationships are worth making 'sacrifices' for, that a woman should 'stand by her man', that children from broken homes have dreadful outcomes. All these make women a step closer to that 'ideal' 
set of circumstances.
That's why the best way to tackle this is through tackling perpetrators and getting more help for women to leave and to STAY left. Heaping moral outrage on them will do little because they won't even recognise it's aimed at them until it's too late. They don't see it the way you see it. And often it takes months out of a relationship for a woman's perceptions to return to normal. Women who manage to stay away from their abuser for a protracted length of time tend NOT to return. It's the ones who can't avoid their abusers who struggle and often go back. This is why cutting refuge places, cutting social fund grants, cutting social housing, etc are so important. They trap women. And it's made worse by courts who insist that abuse toward a woman is no reason for a child not to have contact - seeming to completely miss the point that this prevents the woman from truly recovering and so renders her and therefore her children at greater risk for abuse in the future. There have been a couple of cases here on MN where the the family courts have insisted a child has contact with an abusive man who has been abusive to them as well as their mother. If the 'experts' say it's ok, how can we judge a woman so harshly when she may have had years of grooming to reach the point where she thinks it's ok?
None of this deals with the example of the women who made a decision to put up with her children being abused in the first few weeks of a relationship but then I honestly don't believe that is commonplace.
Nor do I think that the woman's suffering trumps the child. I have no problem with SS intervening to keep a child safe if the mother is incapable of doing so. The child has to come first. However, it makes more sense for the child if the mother can be helped to reach the point where she CAN stand up for the child. So giving SS or the courts the power to remove the man from the house and ban him from contact for 6 months WITHOUT the consent of the mother, would be a good step. Tag the man to make sure he won't flout it (as early on in the separation a mother who could in 6 months time lay down her life for her child might at this early stage let her abuser back in and he knows that). Mandatory prison sentences for DV instead of the usual caution. Lots of things can be done. But aren't.