Can a non-custodial parent get custody of a child iwhen the child is exposed to second hand smoke in the custodial parent's home in New York State?

If smoking is the only issue, then most likely not. The standard for whether someone is custodial is the best interests of the child, some of those factors include which parent has been the primary caretaker, where the child has been living his/her whole life, as well as health issues.  Cases are very fact specific. Smoking by itself isn't enough. But it is certainly a factor that the Court should be alerted to in any case. Good luck.