How do grandparents get custody

My son’s pregnant ex-girlfriend (19 years old) just move out from his place to live with two girls that are "married to each other". She is not taking care of herself (smoking, emotionally unstable and drugs) and I am worried the baby will suffer. Her mother is a crack addict and lost custody of her daughter years ago. Her grandmother who is now deceased raised her. She has no place to live and no high school degree. My wife and I are wealthy; my youngest son just finished high school with a 4.1 GPA and will be going to a private med school (42K a year). We will have five empty bedrooms and the means to bring this child up in a great area with doctors as are neighbors instead of the trailer trash she will live in. What are our rights vs. the mothers? The baby will get the best medical attention and proper schooling. We do not want the mother in our house or near our son and see only hardship for the child if the mother tries to raise her.