All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If what you mentioned about that woman is true, then she is in a very serious situation and is committing some major sins. The Sharee’ah made the husband guardian over his wife, so it is an obligation to advise him to try to put her right, as he will be questioned about her on the Day of Judgment; Allaah says (what means): {O you who have believed, protect yourselves and your families from a Fire whose fuel is people and stones, over which are [appointed] angels, harsh and severe; they do not disobey Allaah in what He commands them but do what they are commanded.}[Quran 66:6]
One thing that will help him to set her straight is taking her away from the corrupt environment in which she lives. If her conduct changes and she is set straight, then this is desirable; otherwise, he should consider divorcing her and not keep such a woman as his wife unless there is a greater benefit.
If he divorces her, she has no right to take custody of the children due to her dissoluteness. He is obliged to make every effort to take the children from her as she may corrupt their religion and conduct, let alone the fact that she may cause physical harm to them since, as you mentioned, she drinks and leaves her children hungry and neglects them despite their young age.
For more benefit, please refer to Fatwa 90109.
Allaah Knows best.