Hello
As a Duke alum, and interviewer, here are some observations:
As others point out, the 28 ACT is fairly low for Duke. My guess is that this would put you in the bottom 10-15% of accepted students. However not is all lost. Your GPA looks quite stellar. Good news is that Duke weighs GPA and Test scores equally. If you compensate with getting high scores in the other areas (reccs, essays, ECs, etc) then having a low ACT score won’t completely sink you.
See details here on the 6 point rating process: http://www.dukechronicle.com/article/2015/03/ferpa-request-gives-inside-look-duke-admissions-process
Your application will undoubtedly go before committee for deliberation. Since your mom is an alum, it will also get an extra review. Your best chance of admission is via applying ED. I would definitely not recommend waiting until the RD round if Duke is your first choice.
Overall I agree with your counselor, I think you have a chance at Duke, but only via ED. My suggestion is to apply ED and then focus on writing killer essays.