Joint custody is out of the question since he and your mother are separated and not on good terms. Further, he lives in another State. As for visitation, he doesn't really sound like a candidate for it. If his lifestyle is as you've described, I don't see a court granting him visitation.
If the parents are alive and not unfit as parents, the court would not give the children to a grandparent for custody, especially if abusive and unfit. In fact, visitation to such a grandparent would be a stretch. Consult a family court attorney.
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No. In New York, grandparents have no standing to sue for custody unless the biological parents are dead or deemed unfit by a court. All the details you provide would have to end up in an order finding these people unfit for another family member down the line to get custody.