Actually, the most common resolution employed by the Court in a "split custody" arrangement such as your is to calculate each parent's child support obligation for the child in the custody of the other parent, and to offset the two, resulting in the net difference being paid by the parent with the higher income. If both parents have equal income, this would result in a "wash", but if either parent earns more than the other, the parent with the higher income will pay the resulting difference to the other. You should consider filing two petitions; one alleging a change of circumstances and seeking to modify your support obligation; and the other seeking an order of support for the child living with you. Both petitions will be dealt with together by the Court in determining a final support obligation.
Mr. Rosen practices matrimonial and family law in Great Neck, NY. His response here is not legal advice and does not create an attorney/client relationship. The response is in the form of legal education and is intended to provide general information about the matter in question. Many times the questioner may leave out details which would make the reply unsuitable. You are strongly advised to confer with an attorney in your own state to acquire more information suited to your particular circumstances.