Ok, what would the gist of this suggested statute be? In other words, define, albeit briefly, what this new crime would be.

As for me, I suggest the mother in question in not exactly in running for mother of the year, I would be hard press to define a crime to cover her behavior.

I suggest that while criminal conviction may not be possible, public ridicule would be in order.

You're right. It's completely the fault of the guys she brings home. Although, if you bring a violent felon into your house, you may have culpability problems in regards to child endangerment.
The dead child had ten broken ribs which were broken prior to his getting his skull crushed. Perhaps she's a bit negligent, as well.

The authorities took away her other kid. I imagine it's because they don't think she's quite up to snuff as a mother.

It's not an exercise in theoretics. There's an actual little dead infant.

There's the legal concept of being guilty of a crime by being criminally negligent. I'd suggest that by the mother's criminal negligence in a case like this she'd be whatever Florida calls an accessory to the crime.

In Georgia they've done away with legal technicalities such as "accessory" - if you participate in a crime in any way, you're guilty of the crime. About 15-years ago, a woman brought home a man who, she claimed, intimidated her. The man eventually killed the woman's little girl, then boiled her to remove her flesh, then the man and the mother scattered the remains in one place, and the bones in another. Both the man and the mother were charged with murder. The woman tried a battered woman defense, but the jury found both of them guilty, in part because she was criminally negligent in bringing the guy into the home. IIRC, he got a death sentence and she got mandatory life.