@Anonymous wrote: "what recourse might we have if the employer is unwilling to issue the requested letter?"
My (unofficial) opinion is that your daughter filed her NJ tax return correctly. Number one, she never lived in or actually worked in NJ. In fact, since she continued to work in NY due to her employer's own COVID rules, I think a case could well be made that NY was her de facto "assigned work location." IMO you're correct that her employer should not have withheld NJ taxes from her pay.
In fact, it's evident from what you were told by NJ that they would issue a refund if they had the necessary documentation from her employer. So it seems that NJ agrees with your interpretation of the rules.
Unfortunately, since her employer won't cooperate, I think your only recourse is to appeal again to the State of NJ, and describe the whole situation in detail as you've done here. The letter you received from NJ should contain appeal instructions.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
