Tell your parents to consider the Thayer for A-Day, PPW, and Graduation. It is a pleasure to be inside of the gate for all occasions, especially graduation week. This is true even if you are a military ID card holder. There is no 'fastlane' on big event days.
Also, being at the Thayer means that the cadet (Future You) can walk over to meet them for drinks and dinner overlooking the Hudson at the Zulu Lounge if you have down time during Grad Week or PPW or Ring Weekend. The price is high--but you pay for the ease and proximity. For graduation the Thayer will say it is 'no return' but if something happens along the way, you will either get refunded or you can find someone on the West Point Moms (or Dads) page or off the waiting list who will gladly take those rooms. I booked three rooms at the Thayer at 0900 on R-Day in 2012 standing with a bunch of dad's trying to make the same call at the same time on the patio of Ike (In those days, 0900 on R-Day was the first moment reservations.) It seemed like a lot of money upfront--but I was so happy 47 months later to have valet parking and a shuttle for my handicapped mama from the door of the Thayer to the Michie Stadium.
I did not do the Thayer for R-Day with the Baby--because it required booking two nights and I felt like I only needed one. I could have used the night of R-Day.
You all made the right choice for your R-Day. You should get there early--and you have to eat breakfast even though your stomach will be in knots--and then it is hot all day and a lot of standing (for the parents, too).