I'm simply stunned that parents can be prosecuted for this. Another wtf America moment.
Instead, the prosecutor decided to charge her with "contributing to the delinquency of a minor" which is a broad catch-all category for doing things that might harm a child. She was not found guilty of this crime either. Instead, her lawyer advised her to agree to punishment for the crime because if it went to trial there was a CHANCE that she would lose custody of her children.
The problem here is not in the law nor in the outcome of a court case. The problem lies in the structure of the legal system. Prosecutors wield enormous power by virtue of their ability to decide whom to charge and for what. The penalties for losing are so great that nearly all (around 95%) cases are settled rather than contested before a judge or jury.
Many laws in the US are purposely vague and up to the interpretation of the police. The mother was charged with "contributing to the delinquency of a minor" (http://legal-dictionary.thefreedictionary.com/Contributing+t...), which can be used against anyone that does something that might possibly result in a child being adversely affected in some way.
The unfortunate part of life in the US is that the average person breaks a few dozen laws every day, and it's really important not to upset the police in some way that they'll take notice of you and start charging you with crimes.