The court will look to the best interest of the child. While it is important for both parents to be involved in their child's upbringing, the fact that the father of the child has these issues will mitigate his rights. Of course, you will need to prove these allegations. You can compel him to attend a drug test and a psychological evaluation.
I recommend you seek out a local attorney to review this matter as it could be complex with retaining experts and court appearances.
Sign up to receive a 5-part series of useful information and advice about child custody law.