All you'd need is to send a letter to the court withdrawing your petition (assuming the opposing party hasn't filed a counter-petition). That said, the only aspect where your children would be "involved" is via an interview in a lawyer's office & possibly (IF the case goes to trial) a private interview in the Judge's chambers outside of the presence of the parents. Before deciding anything, it may behoove you to schedule a consult with a NYC Child Custody lawyer.