I agree with my colleagues. If she is LIVING in New Jersey, then it will be easier for the Courts to enforce a judgment against her there. If you're really concerned, hire an attorney with licenses in both states, or at least consult with one with both. That is pretty common.
This does not constitute legal advice or the engagement of my services as an attorney.
Yes, more facts are needed, but assuming that her stay in NJ is not temporary and she no longer has an actual dwelling in NY that she returns to, then New Jersey is the safer bet.
This response does not create an attorney-client relationship and is not intended to provide legal advice for your specific situation.