I don't think it's too far, if that is truly the traditional way your family does things.
I live in the South, but never required my kids to say ma'am or sir, but the teachers
at their school set them straight, and have them saying it (which is fine by me).
I am, however, puzzled as to why you didn't instill this in her 12 years ago when
she was younger, and more willing to listen to you. To suddenly want her to do
it 16 may not work out.