Here’s what I suggest: Have your father write a letter (or write it for him & have him sign it) that explains why he is allowed to file head of household, and include a printout of the IRS training document I linked to, with the part I quoted highlighted. Write something like this:
“I filed as head of household for tax year 2021 because I was “considered unmarried” for tax purposes. According to the enclosed IRS document, I met the criteria because my wife didn’t live with me during the final six months of 2021; in fact, she has never lived in the United States. I also met the other requirements for filing as head of household.
My wife isn’t able to get a letter from the IRS stating that she didn’t file taxes in 2021 because she has never lived in the U.S., doesn’t have a social security number and is not in any IRS database. She lives in Vietnam. In 2021, she earned $ (you need to enter her earnings here), converted from Vietnamese dong to U.S. dollars as of today’s conversion rate.”
I suggest setting up a Zoom call with a financial aid officer to let them know that you will be sending this letter. Explain that you were told by the financial aid office that your father has to amend his taxes, but that after looking into the situation, it appears that your father was able to file as head of household and should not be required to amend his taxes in order for you to receive financial aid. If the person with whom you speak insists that your father has to amend his taxes, ask to speak with the person’s supervisor.