You need to re post this under family law. This isn't a specific domestic violence issue that you are asking so re post and you will find several attorneys to help you. Good Luck.
The court will typically want to preserve the status quo with who has been the primary care provider for the child. However, your son will want to show the court how involved he has been with his child, and the court will be concerned about mother's alcohol use and how that may be (or has been) a detriment to the child. He will want to consult with a family law attorney in your area. Good luck to him.
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