Now that we are divorced can I stop my spouse from having overnight visits with our kids?

On what basis? You can’t just ask the court to order that your spouse cannot have overnight visits with your mutual child. You have to have a reason that is provable and justifiable. The worse thing you can possibly do is make up stories and lies about your spouse’s unfitness, or “inappropriate behavior” that your spouse has towards the young children.
Many former spouses, mostly wives, make this allegation – that the father should not have overnight visits because he somehow is unfit because of internet activity, or other reasons. This may well be true, but if you cannot prove it, I would be very careful about making this allegation. It could actually cause the court to take custody away from you and give it to your spouse – on the basis that your attempts to keep the child away from the other parent is psychologically damaging to the child and is not in the child’s best interest.
I remember last year when Denise Richards and Charlie Sheen were in the midst of their acrimonious divorce she made similar allegations. She did not want Sheen to have overnight visits. Of course, they live in California, not New York and I am not sure how their divorce was ultimately decided and what Sheen’s parenting rights were. I know she still has custody of the girls. He has since remarried and his wife is pregnant with twin boys. Whether he has overnights with his young daughters with Richards, I don’t know.
But I suspect he does. It is highly unlikely that a court would have granted Richards’ motion without a thorough investigation and hearing. Had he been found to behave inappropriately towards those girls it would have been front page news.
So unless you have basis, my recommendation is don’t make these allegations. In order to hold on to your custody you have to show that you can foster a healthy relationship with the children and the other parent. You cannot appear to be alienating the children from the other parent. This is a basis to change custody.