First, on your federal joint return claim everything. Next, for VA here is the VA reference for your filing status (see below for extract). You should be filing status 3 and file a separate VA return with only your income/deductions. You are correct it doesn't matter where the property is located; you just need to claim your portion of any itemized deductions on your resident Married Filing Separate VA return.
Further, you would likely claim the rental property income/expenses on your separate VA return.
"If you and your spouse filed a joint federal return, but only one of you is a Virginia resident, the resident must use Filing Status 3. When using Filing Status 3, complete your tax return as follows: (1) Compute your federal adjusted gross income as though you had filed separately on your federal return; (2) claim only the personal and dependent exemptions, itemized deductions (if claimed on your federal return), and child and dependent care expense amounts that you could claim if you had filed a separate federal return. If one spouse claimed itemized deductions, the other spouse must also. (3) Be sure to provide your spouse's name and social security number in the spaces included on the return for that information."
The best way to handle filing joint federal return and a separate state return is to use a TurboTax desktop product. There you can create and e-file your joint federal return and then create a "Mock" separate federal return with only your income/deductions that will then flow to your VA separate return. You will not file the mock federal return and you will need to print/mail your VA return since you are not actually filing the corresponding federal return. Here is a link that will be helpful.
For NY you have the option to file a joint NY return as if both are residents. Here is the NY reference. However, you also have the option to file a separate NY return for your spouse as well. Again in the desktop version you can create the "Mock" federal separate return for your spouse which will flow to the NY separate return. You can create the joint NY return for comparison there in the desktop if you prefer to see which yields the best tax outcome.
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