UIFSA Procedural Guidelines Handbook
http://www.ncjrs.gov/pdffiles1/ojjdp/189181.pdf
The first link deals with the child support issue itself. While it was initially setup to manage child support cases when parents live in separate states, it also covers, at the federal level, child support issues when there is more than one order involving a child.
The second link deals with the custody aspect. Same situation, wrote to manage cases where parents live in separate states, but applicable at the federal level to cases where there are competing custody orders. After these laws were enacted, there can only be one child support order valid at a time, and one custody order valid at a time. In order to modify a pre-existing child support order, it has to be done through the court having jurisdiction and they will not retroactively change the support order unless the order in question was erroneously done. Same with custody.
Specifically for NY state, see link below. See Paragraph K.8.
OCSE STATE PROFILE - View Page