Thank you for your question. I look forward to working with you to provide you the information you are seeking for educational purposes only.
As you may know, custody/visitation
in NY is a completely separate issue from child support in NY. Child support is due whether the paying parent ever gets to see the child. Child support is money due to the custodial parent
for helping them provide for the child, it is not something that is due to the child (even though we hear parents argue all the time they want to give the payment to their child, the courts do not see it that way). You can argue for a reduction of support based on your significant decrease in income, which is a legal basis to secure a reduction, but arguing not seeing the child or she is not sending money to the child generally are not arguments accepted by the court.
If the judge is going to allow her to testify by telephone, that is the judge's discretion. If you need her to testify as to documents, then you need to send her a copy of each document you want to question her about in advance of the hearing.
You could also seek to try to schedule a deposition by sending a deposition subpoena, but the court can make you go to where she is located to depose her with a court reporter (you would bear the cost of taking that deposition) and in that way you could personally show her the documents and question her under oath and the transcript of that deposition can then be used when you question her in the hearing over the phone. The deposition can also give you advance notice of her statements so you can put together documents to disprove or discredit her statements when she testifies by phone in the hearing before the judge.
Other than the deposition, you would have to subpoena her and if the judge allows her to appear by phone you need to attach all of your documents you want to question her about to the subpoena.