What's more fucked up is that if you put this woman in jail and put the kid in foster care, you'd be punishing the kid more than the mother.

Even if that's true, that not an argument that she shouldn't be punished. It's just an argument that foster care is yet another facet of your government that is abjectly failing you through incompetence or corruption.

Leaving this boy under the heel of that woman (literally) is only vastly increasing the chance he grows up to be a violent criminal of the highest order, with an immense reservoir of resentment and an inherited understanding that unlimited violence against helpless beings is an acceptable emotional outlet. He might be one of the rare few who can channel that suffering into something that doesn't offload that suffering on others, but that would make him a statistical anomaly. Foster care should at the very least provide a level of care that is better than the level of abuse that makes psychopaths. And everyone should care if the government is fucking that up because you don't want your kids' peer group to be full of damaged nutcases.