She should be go to court and move to enforce any outstanding orders. It will the quickest resolution to the matter. Good luck.
I have been a criminal attorney in New York for almost 25 years. website: Brooklynlaw.net Phone #: 718-208-6094 email: email@example.com. This answer is only for informational purposes and is not meant as legal advice.
She needs to file a court action. Contacting the court by phone or mail will not result in any action; she should consult with an attorney as soon as possible in order to file the proper papers to enforce the prior orders. The maintenance should be the easiest part of the enforcement; if he cannot prove he has paid the amount ordered, he will owe her arrears which can be reduced to judgment and collected from his income, and probably will have to pay her attorney's fees as well.
What struck me about your question is that It is unusual that your daughter does not have custody of her daughter. I am left to assume there are serious issues about either her parenting skills or personal issues. But to answer your question at its basic level, your daughter needs to bring her ex to court to get the maintenance money and needs to file a separate petition to ensure privacy of your daughter's phone conversations with her child.
Your daughter needs to engage the services of a family law attorney to move forward and file a petition with the Court to enforce the terms of her order. The ex-husband's attorney is under no obligation to communicate with your daughter directly. If the ex-husband is working, it should be fairly easy to garnish his wages for the support monies.