Depends on the professor. If I thought the professor was a reasonable person on this issue, I'd have a discussion, pointing out that people, including the professor, have a right to be called by the term they choose, in the hopes that the professor would relent.
If the professor seems adamant on this issue, and you suspect using "Mrs." might affect your grade, I'd use "Ms" on everything turned in to the professor.
If Mrs. Vazquez happens to see any of that material, I'd just explain that my professor insists on "Ms" with no exceptions, and since I need a passing grade in this course, that's what I used. Any documents submitted to the museum would of course have her preferred title of "Mrs." substituted.
And if either of them complained about it after that, I'd refer them to each other and take myself out of the battlefield. Because their real problem wouldn't be with me and I wouldn't want to waste my life energy sorting out the mess. They are the ones causing the problem; let them fix it.