If you're a Resident of New York, report all your income there.
File a separate Non-Resident State return to New Jersey, reporting only the income you earned there/tax paid there. Nothing else gets reported there. Your mock Federal return should only have this info to flow into NJ.
In your joint NY resident return, report everything. Just make sure that you enter 'Taxes paid to another taxing authority' as JUST the amount of NJ tax paid, and you may need to also enter the amount of NJ income the tax was based on.
Here's more info on How to File a Non-Resident State Return.
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