In answer to your question on taxability of alimony, I don't think your client has to pay tax to NY. Here is a link to an old court case on the subject.

 chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://www.tax.ny.gov/pdf/memos/income/m85_7i.pdf

as far as NY withholding I would think it would be easer to just file a nonresident NY return to get back the NY withholdings