My response:
Thanks for getting back to me, Jeter.
You have two issues - - one is divorce, and the other is child custody, visitation and support for the child (the Child Issues).
THE DIVORCE - -
Because of the length of time you've lived in Jersey, and if you file for divorce, it'll have to be filed in Jersey. New York is no longer an option for you since New York no longer has jurisdiction over you. If she files for divorce, she will only be able to in New York. Then, you can either choose to appear for that part, or let it go to a "Default Judgment". If you file for divorce in Jersey, she can either choose to appear, or allow the matter to go to a Default Judgment". But, if you file, no child issues can be heard by the Jersey court.
THE CHILD ISSUES - -
Since the child resides in New York, that State has jurisdiction over the child. Therefore, you can only file in New York concerning this issue. You can't file in Jersey concerning this issue because Jersey does not have jurisdiction over the child.
She, however, can file in New York concerning both of the above issues, and have them dealt with at the same time because the State court has jurisdiction over her and the child.
THE SUMMARY - -
You, if you choose to be the one doing all of the various filing, will have to file in both States - - Jersey for the divorce and New York for the child issues.
Good luck to you Jeter, and I sincerely hope that these matters work out for you.
Thanks for contributing to the Boards, also.
IAAL